Moving Gjennomsnittet At Endringer Farge

Lawn Bowls - Spillets Innledning Du vil ikke finne en omfattende beskrivelse av reglene og målene for Lawn Bowls her, men forhåpentligvis kan jeg gi et innblikk i spillet vårt og hvordan det spilles. Du kan også lese litt om historien til spillet på vår Lawn Bowls History-side. Som de fleste sportsskåler bruker sitt eget språk, så jeg har gitt en ordliste av vanlig plenskålsspråk nederst på denne siden. Jeg har også inkludert en Lawn Bowls Ofte stilte spørsmål side. Svarene på disse spørsmålene refererer til Scottish Bowling Association regler, men vil i stor grad lignes i andre nasjonale foreninger. Ta en titt på dem, noen av dem kan overraske selv de mest erfarne bowlers. Spille lekeskålspill Det er sagt at Lawn Bowls er et spill som kan spilles av alle i alderen fra ni til nitti og i min tid i spillet har jeg kommet over flere nonagenarian spillere. Det har en tendens til å ha et crusty, quotolds folks gamequot image skyldes i stor grad bruken av sponsorer som Saga og over 55s forsikringsselskaper. Virkeligheten er noe annerledes, og på fylkeskommunen i Skottland er gjennomsnittlig spillernes alder trolig et sted i trettiårene. Konkurransedyktig bowling kan være et utmattende spill, og i spillerne forventes spillere å utføre i tre til fire timer uten pause. Under disse spillene kan de gå to eller tre miles og bøye opp og ned mer enn 100 ganger. Det er ikke rart at bowlere tradisjonelt lider av både rygg og kneskader. Legg til det konsentrasjonen og innsatsen som kreves, og du kan se hvorfor vi trenger et sete og et par øl etter kampen. Spillet spilles på en Bowling Green. Overflaten er generelt gress, men i noen av de varmere, tørrere landene blir kunstige overflater i stadig større grad brukt. I land med lange vintre, som Storbritannia og Canada, har mange innendørs bowling sentre sprang opp der spillet spilles på et teppe som overflate. Mens vekten som kreves for å levere skålen, endres på disse flatene, er spillets regler og mål i det vesentlige det samme. Lawn Skåler er tilgjengelige i forskjellige størrelser med en mellomstor manneskål som er mellom 116 mm og 131 mm i diameter. De er laget av et hardt plastmateriale som er i stand til å tåle den konstante kontakten mellom boller under lek. Deres vekt bør ikke overstige 1,59 kg. Inntil 2001 var alle pleneskåler enten svarte eller brune i farge. Reglene er nå endret for å tillate boller i nesten hvilken som helst farge, og produsentene har tatt opp utfordringen ved å produsere boller i omtrent alle farger som er tenkelige, selv rosa. Bunnlinjen er at fargene på bollen ikke hjelper deg med å spille noe bedre I løpet av et spill leverer (ruller) sine boller opp den grønne og prøver å fullføre nærmest en mindre hvit ball kalt quotJackquot. En bowlinggrønn er normalt firkantet, og Scottish Bowling Association-reglene sier at den ikke skal være mindre enn 34 meter og ikke mer enn 40 meter i retning av lek. Det er omgitt av et grunt grøft. Omkretsen av grøften er omgitt av en bank, som ikke skal være mindre enn 230 mm over overflaten av grønt. Den grønne er normalt delt inn i seks quotrinksquot slik at seks spill kan skje samtidig. Rinkene skal ikke være mindre enn 5,5 meter eller mer enn 5,8 meter bred. Overflate slitasje spres ved å flytte rinkinnstillingene sideværts og ved å endre spilleretning hver to eller tre dager, spiller enten over det grønne eller opp og ned. Rinkekstremiteter er markert av grensemarkører med midtpunktet for hver av dem er angitt med en kvoteringskvot som også bærer et nummer til rinken. Rinkene er nummerert fra 1 til 6. Spillerne leverer sine boller fra en ende til en annen under en kvotering, da når de er ferdige, svinger de seg og spiller tilbake igjen. Plenskåler er ikke sfæriske, de er formet på den ene siden slik at de følger et buet spor til stikkontakten. De har et merke for å angi hvilken side forspenningen er påført. Som vist på diagrammet kan bollene leveres på kvotens kvote (høyre side av rinken) eller kvoteteksten (venstre side av rinken) avhengig av spillerens preferanse eller hvor skåler som allerede er spilt, befinner seg. (Diagrammet refererer til en høyrehendt bowler. Fore og Back vil bli reversert for en venstrehåndet bowler.) Den buede banen hjelper spilleren til å finne en måte forbi boller som har blitt levert kort av jacken. Legg merke til at boller kan reise utenfor grensen til rinken i løpet av deres kurs så lenge de kommer til å hvile innenfor disse grensene. Spillerne må stå på en gummimatte når de leverer bollen. Matten er plassert på midtlinjen av rinken med sin forside ikke mindre enn 2 meter fra bakre grøft eller mindre enn 25 meter fra grøften. Dens posisjon er valgt av spilleren som kaster jacket for å starte enden. Når en bolle blir levert, må en av føttene være på eller over matta når den forlater hånden. Manglende overholdelse av dette kan vurderes som fotfeil. I løpet av en slutt blir bollen nærmest Jacken referert til som quotthe shotquot. Du kan høre spillere på matten spør, quote Hvem lyver shotquot. Spilleren som først leverer jacket, må sørge for at den er riktig sentrert. Hvis det kommer til å hvile innen to meter fra grøntens forkant, må det flyttes ut til et merke i den avstanden. Spilleren som leverer jacken, kan velge lengden for å spille den, men den må fullføre minst 23 meter i en rett linje fra forkant av matten. Spillerne skiftes da for å levere sine boller. Når alle bollene er levert, teller antall kvoteringskvoter. Et skudd er en bolle som er nærmere jacken enn noen av dine motstandere boller. For eksempel, hvis du har tre skudd nærmere jacken enn noen av dine motstandere boller, scorer du tre skudd i den enden. I dette bildet, ved avslutningen av en typisk slutt på boller i en single-kamp, ​​har hver spiller spilt fire boller. Spilleren som bruker de svarte bollene, har to boller nærmere jacken enn motstandernes nærmeste blå bolle. Dette betyr at spilleren med de svarte bollene teller to skudd. Typer av Lawn Bowls Spill og Matcher Spill av boller kan innebære singler spill eller lag av to i par, tre i trippel eller fire i quotrinksquot spill. Kampene involverer vanligvis en rekke lag fra en klubb som spiller en annen klubb. For eksempel kan en kamp innebære seks baner eller 24 spillere (6x4) per lag. Jacken kan flyttes av bollene i løpet av spillet. Når en bolle flytter kontakten, blir den igjen i den nye stillingen, forutsatt at den forblir innenfor rinkgrensemarkørene. Det kan også presses inn i grøften med en bolle. I dette tilfellet forblir det i grøften, og spillerne må prøve å spille sine boller så nært som mulig til kappen, på kanten av den grønne, uten å falle i grøften. En bolle som beveger jacken er merket med kritt og klassifisert som en quottoucherquot. Hvis det berører stikkontakten før det faller inn i grøften, forblir det der, forblir kvotekvoten og kan være med i det endelige skuddtallet. En berøringsrør som forblir på rinken og senere kjøres inn i grøften med en annen bolle, er også en levende bolle. En bolle som går inn i grøften, og som ikke har rørt jacken, er klassifisert som quotedadquot og den er fjernet. Alle boller som slutter utenfor rinkens sidegrenser er døde. Lawn Bowls Tactics Bowls er et svært taktisk spill. Dette er en av attraksjonene. Det handler ikke alltid om kvoteringskvoten nærmest kappen. Spillere må hele tiden forutse hva skudd motstanderne kan vurdere å spille neste. For eksempel når et lag har noen boller bak hodet, (bak jacket), kan motstanderne se behovet for å legge en bolle blant disse for å dekke muligheten for at jacken blir flyttet. På samme måte, hvis en side allerede ligger i skuddet, kan de velge å spille et vaktskudd kort av målområdet for å hindre at motstanderne flytter noe. Dette er bare to eksempler, og det er mange andre situasjoner, for mange for å diskutere her, hvor taktikk kommer inn i spill. Typer av skudd i bowling Det er i utgangspunktet fire forskjellige typer skudd, eller levering i Lawn Bowling. Disse er. En tegningsserie er den vanligste og det er egentlig hva spillet handler om. Dette bildet er det spilleren prøver å spille med den nøyaktige vekten som er nødvendig for å fullføre nærmest jacken eller til et punkt på den grønne diktert av strategi eller taktikk. Dette skuddet regnes ofte som den mest dyktige. The Yard On The Quotard Onquot-skudd er når spilleren leverer en bolle med nok vekt til å bære den til en hage eller to forbi målet. Målet med dette skuddet er vanligvis å trekke jacken vekk fra motstandernes boller mot din egen eller å skyve en bolle ut av quotheadquot og ta sin plass. Dette blir ofte referert til som et quote - og liequot-skudd i Skottland. Running Shot eller Ditch Length Shot Running Shot er en som bruker mer vekt enn verftet på. Formålet med dette skutt er å fjerne motstandere boller fra hodet, for å flytte jacken til grøften eller for å finne et annet resultat som krever at skålen skal spilles med vekt. Dette kan være et vanskelig skudd å spille som linjen (bias) som kreves for å komme til målendringer med forskjellig vekt. Stasjonen er sannsynligvis det mest spektakulære skuddet på bowlinggrønt. En stasjon er når spilleren leverer bollen med høy hastighet og med maksimal vekt, slik at han kan slå hodet eller målet med full kraft. Hensikten med dette skuddet kan være å helt fjerne motstandere skåler fra hodet eller fra rinken eller å koble jacket til grøften. Det er også vanlig når en spiller har noen få skudd mot ham. I dette tilfellet er objektet å ødelegge hodet eller å kvitte seg med enden ved å kjøre jacken ut av rinken. Dette kan være et veldig effektivt og skremmende skudd å ha i din armory, men mange spillere har problemer med å styre retningen når de konsentrerer innsatsen på så mye vekt. Vel, det er en kort introduksjon til spill av boller som burde gi deg en ide om hva det handler om. Forhåpentligvis, for de av dere som ikke spiller spillet, men ser det på fjernsyn, vil det gjøre din visning morsommere. Hvis du har spørsmål eller kommentarer på ovenstående, eller hvis du ser noen feil eller skrivefeil, er du velkommen til å email meg, men husk at vi ikke er en offisiell organisasjon. Vi kan ikke svare på formelle spørsmål om reglene i spillet. Lawn Bowling GlossaryGASES, LIQUIDS and SOLIDS bruk av partikkelmodellen for de tre tilstandene av materiepartikkelmodeller, som beskriver, forklarer egenskapene til gasser, væsker og faste stoffer. Doc Browns Chemistry KS4 vitenskap GCSEIGCSE Revisjonsnotater Sammenligning av egenskapene til GASES, LIQUIDS og SOLIDSSTATNINGER AV MASJONSVIKTIGE REVISIONSNOTTER Del 1 Den kinetiske partikkelmodellen og beskriver og forklarer egenskapene til gasser, væsker og faste stoffer, tilstandsendringer og løsninger (avsnitt 1a til 3d) Du bør vite at de tre tilstandene er materielle, flytende og gass. Smelting og frysing finner sted ved smeltepunktet, koking og kondensering finner sted ved kokepunktet. De tre tilstandene av materie kan representeres av en enkel modell der partiklene er representert av små faste sfærer. Partikkeltorien kan bidra til å forklare smelting, koke, frysing og kondensering. Mengden energi som trengs for å endre tilstanden fra fast til flytende og fra væske til gass, avhenger av styrken av styrkene mellom stoffets partikler og arten av partiklene som er involvert, avhenger av typen av binding og stoffets struktur. Jo sterkere kreftene mellom partiklene er, desto høyere smeltepunkt og kokepunkt for stoffet. For detaljer, se struktur og bindingsnotater. Den fysiske tilstanden et materiale vedtar avhenger av dens struktur, temperatur og trykk. Statlige symboler brukt i ligninger: (g) gass (1) væske (aq) vandig løsning (er) fast vandig løsning betyr noe oppløst i vann De fleste diagrammer av partikler på denne siden er 2D-representasjoner av deres struktur og tilstand. Eksempler på de tre fysiske STATER AV MATREGASER, f. eks luftblandingen rundt oss (inkludert oksygen som trengs for forbrenning) og høytrykksdampen i dampkondensens kjele og sylindere. Alle gassene i luften er usynlige, fargeløse og gjennomsiktige. Vær oppmerksom på at dampen du ser utenfor en kjele eller damplokomotiv, faktisk er fine, flytende dråper med vann, dannet fra den utdrevne dampgassen kondenserer når den møter kald luft, statens forandring av gass til væske (samme effekt i tåke og tåkeformasjon) . Væsker, f. eks. vann er det vanligste eksempelet, men det er også melk, varmt smør, bensin, olje, kvikksølv eller alkohol i et termometer. SOLIDER, f. eks. stein, alle metaller ved romtemperatur (unntatt kvikksølv), gummistøvler og de fleste fysiske gjenstander rundt deg. Faktisk er de fleste gjenstander ubrukelige med mindre de har en solid struktur. På denne siden er de grunnleggende fysiske egenskapene til gasser, væsker og faste stoffer beskrevet i form av struktur, partikkelbevegelse (kinetisk partikkeltema), effekter av temperatur og trykkendringer og partikkelmodeller pleide å forklare disse egenskapene og egenskapene. Forhåpentligvis vil teori og faktum matche opp for å gi studentene en klar forståelse av den materielle verden rundt dem når det gjelder gasser, væsker og faste stoffer som kalles de tre fysiske tilstandene av materie. Statens endringer som kalles smelting, smelting, koking, fordampning, kondensering, flytende, frysing, størkning, krystallisering beskrives og forklares med partikkelmodellbilder for å hjelpe forståelsen. Det er også omtale av blandbare og ublandbare væsker og forklarer betingelsene flyktig og volatilitet når den påføres en væske. Disse revisjonsnotatene om saksforholdene skulle vise seg å være nyttige for de nye AQA, Edexcel og OCR GCSE (91) kjemifagkurs. Delindex for del I-seksjoner (denne siden): 1.1. De tre tilstandene, gassliquidsolid partikkeltheismodeller De tre tilstandene er materielle, flytende og gass. Enten smelter og fryser kan finne sted ved smeltepunktet, mens koking og kondensering finner sted ved kokepunktet. Fordampning kan finne sted ved enhver temperatur fra en flytende overflate. Du kan representere de tre tilstandene med materie med en enkel partikkelmodell. I denne modelldiagrammer er partiklene representert av små faste sfærer (elektronstrukturen ignoreres). Kinetisk partikkelteori kan bidra til å forklare tilstandstilstendigheter som smelting, koke, frysing og kondensering. Mengden energi som trengs for å endre tilstanden fra fast til flytende eller fra væske til gass, avhenger av styrken av kreftene mellom partiklene av stoffet. Disse kreftene kan være relativt svake intermolekylære krefter (intermolekylær binding) eller sterke kjemiske bindinger (ionisk, kovalent eller metallisk). Arten av de involverte partiklene avhenger av typen kjemisk binding og stoffets struktur. Jo sterkere de attraktive kreftene mellom partiklene, jo høyere smeltepunktet og kokepunktet for stoffet. HVAD ER DE TRE STATERNE AV MATERIALET De fleste materialer kan bare beskrives som en gass, en væske eller et fast stoff. HVORFOR ER DE SOM DET ER Bare å vite, er det ikke nok, trenger vi en omfattende teori om gasser som kan forklare deres oppførsel og gjøre spådommer om hva som skjer, f. eks. hvis vi endrer temperatur eller trykk. Hvordan kan vi forklare hvordan de har vi trenger en teoretisk modell, f. eks. partikkelteori som støttes av eksperimentelle bevis. KAN PARTIKEL MODELLER HJELP OSS FORSTÅR ​​DERES EGENSKAPER OG KARAKTERISTIKKER HVOR ER DET VIKTIG Å VITE EGENSKAPER AV Gasser, Væsker og faste stoffer Det er viktig i kjemisk industri å vite om oppførsel av gasser, væsker og faste stoffer i kjemiske prosesser, f. eks. hva skjer med de forskjellige tilstandene med endringer i temperatur og trykk. Hva er KINETISK PARTIKEL TEORIEN av gasser, væsker og faste stoffer Den kinetiske partikkeltorien om tilstandene av materie er basert på ideen om alt materiale som eksisterer som svært små partikler som kan være individuelle atomer eller molekyler og deres interaksjon med hverandre heller ved kollisjon i gasser eller væsker eller ved vibrasjon og kjemisk binding i faststoffer. KAN VI GJØRE PREDIKSJONER BASERT PÅ DERES KARAKTERISTISKE EGENSKAPER Denne siden introduserer generelle fysiske beskrivelser av stoffer i det enkleste fysiske (ikke-kjemiske) klassifikasjonsnivået, dvs. det er en gass, væske eller et fast stoff. MEN denne nettsiden introduserer også partikkelmodeller der en liten sirkel representerer et atom eller et molekyl, dvs. en bestemt partikkel eller enkleste enhet av et stoff. Denne delen er ganske abstrakt på en måte fordi du snakker om partikler du ikke kan se som individuelt, du bare bulkmaterialet og dets fysiske karakter og egenskaper. Er det BEGRENSNINGER TIL partikkelmodellen Partiklene blir behandlet som enkle uelastiske sfærer og oppfører seg bare som små snookerballer som flyr rundt, ikke helt sant, men de flyr rundt tilfeldig uten å stoppe Selv om partiklene antas å være harde kuler og uelastiske , i virkeligheten er de alle slags former og vri og bøyer seg på kollisjon med andre partikler, og når de reagerer, deles de i fragmenter når obligasjoner bryter. Den enkle modellen antar ingen krefter mellom partiklene, usann, modellen tar lite hensyn til kreftene mellom partiklene, selv i gasser får du svært svake intermolekylære krefter. Partikkelmodellen tar ingen hensyn til den faktiske størrelsen av partiklene, f. eks. ionsmolekyler kan være vidt forskjellige i størrelse, f. eks. sammenligne et etenmolekyl med et poly (eten) - molekyle Mellompartene av partiklene HVA ER DEN GASLEVENDE MATSTATEN HVAD ER GASENS EGENSKAPER HVORDAN GASLEGTE DELARTER BEGRENSER Hvordan forteller den kinetiske partikkelt Theory of Gases Gassens egenskaper En gass har ingen fast form eller volum, men sprer seg alltid ut for å fylle noen beholder - gassmolekylene vil diffundere til all ledig plass. Det er nesten ingen tiltrengningskrefter mellom partiklene, slik at de er helt fri for hverandre. Partiklene er vidt spredt og spredt ved raskt å bevege seg tilfeldig gjennom beholderen, så det er ingen ordre i systemet. Partiklene beveger seg lineært og raskt i alle retninger. og kolliderer ofte med hverandre og siden av beholderen. Kollisjonen av gasspartikler med overflaten av en beholder forårsaker gasstrykk. ved å hoppe av en overflate utøver de en kraft i det. Med økning i temperatur. partiklene beveger seg raskere etter hvert som de får kinetisk energi. Kollisjonen mellom partiklene selv og beholderflaten øker, og dette øker gasstrykket, f. eks. i et damplokomotiv eller volumet av beholderen hvis det kan ekspandere, for eksempel som en ballong. Gasser har en meget lav tetthet (lys) fordi partiklene er så fordelt i beholderen (massefylde for tetthet). Tetthet rekkefølge: fast gt flytende gtgtgt gasser Gasser flyter fritt fordi det ikke er noen effektive tiltrekningskrefter mellom de gassformige partikkelmolekylene. Enkel strømningsordre. gasser gt liquids gtgtgt solids (ingen ekte flyt i fast med mindre du pulver det) På grunn av dette er gasser og væsker beskrevet som væsker. Gasser har ingen overflate. og ingen fast form eller volum. og på grunn av mangel på partikkelsattraksjon, sprer de seg alltid og fyller beholdere (så volum på beholdervolum). Gasser komprimeres lett på grunn av det tomme rommet mellom partiklene. Enkel komprimeringsordre. gasser gtgtgt væsker gt faste stoffer (nesten umulig å komprimere et faststoff) Gasstrykk Når en gass er innestengt i en beholder, vil partiklene forårsake og utøve et gasstrykk som måles i atmosfærer (atm) eller Pascals (1,0 Pa 1,0 Nm 2), trykket er forcearea dvs. effekten av alle kollisjonene på beholderens overflate. Gasstrykket skyldes kraften skapt av millioner av påvirkninger av de små, individuelle gasspartiklene på sidene av en beholder. For eksempel dersom antall gassformige partikler i en beholder dobles, blir gasstrykket doblet fordi fordobling av antall molekyler dobler antall påvirkninger på beholderens side, slik at den totale slagkraften per arealområde også blir doblet. Denne fordoblingen av partikkelpåvirkningen dobler trykket er vist i de to diagrammene nedenfor. Hvis volumet av en forseglet beholder holdes konstant og gassen innsiden er oppvarmet til en høyere temperatur, øker gastrykket. Årsaken til dette er at når partiklene oppvarmes får de kinetisk energi og beveger seg i gjennomsnitt raskere. Derfor vil de kollidere med sidene av beholderen med større kraftpåvirkning. slik at trykket økes. Det er også større kollisjon med sidene av beholderen, MEN dette er en mindre faktor sammenlignet med effekten av økt kinetisk energi og økningen i gjennomsnittskraften. Derfor en fast mengde gass i en lukket beholder med konstant volum, jo ​​høyere temperatur jo større trykk og jo lavere temperatur er, desto mindre er trykket. For beregning av gasstrykkstemperaturen se Del 2 CharlessGayLussacs Law Hvis beholdervolumet kan endres, ekspanderer gassen lett etter oppvarming på grunn av mangel på partikkelattraksjon, og kan lett avtrekkes ved avkjøling. Ved oppvarming får gasspartikler kinetisk energi. Flytt raskere og treffer sidene av beholderen oftere. og betydelig, de treffer med større kraft. Avhengig av beholdersituasjonen vil enten eller begge trykk eller volum øke (omvendt ved kjøling). Merk: Det er gassvolumet som utvider IKKE molekylene, de forblir i samme størrelse. Hvis det ikke er noen volumrestriksjon, er ekspansjonen på oppvarming mye større for gasser enn væsker eller faste stoffer fordi det ikke er noen signifikant tiltrekning mellom gassformige partikler. Den økte gjennomsnittlige kinetiske energien vil gjøre gasstrykket stiger og så vil gassen forsøke å ekspandere i volum dersom det tillates å f. eks. ballonger i et varmt rom er betydelig større enn den samme ballongen i et kaldrom For beregning av gassvolumetemperaturer se Del 2 CharlessGayLussacs Law DIFFUSION i gasser: Den naturlige raske og tilfeldige bevegelsen av partiklene i alle retninger betyr at gasser lett sprer seg eller diffunderer. Nettbevegelsen til en bestemt gass vil være i retning fra lavere konsentrasjon til en høyere konsentrasjon, nedover den såkalte diffusjonsgradienten. Di ffusjon fortsetter til konsentrasjonene er jevne i hele gassbeholderen, men ALLE partiklene fortsetter å bevege seg med sin allment eksisterende kinetisk energi. Diffusjon er raskere i gasser enn væsker der det er mer plass til dem å bevege seg (eksperiment illustrert nedenfor) og diffusjon er ubetydelig i faststoffer på grunn av den tette pakningen av partiklene. Diffusjon er ansvarlig for spredning av lukt selv uten luftforstyrrelser, f. eks. bruk av parfyme, åpne en krukke med kaffe eller lukten av bensin rundt en garasje. Graden av diffusjon øker med økning i temperaturen som partiklene får kinetisk energi og beveger seg raskere. Annet bevis for tilfeldig partikkelbevegelse inkludert diffusjon. Når røykpartiklene blir sett under et mikroskop, ser de ut til å danse seg når de lyser med en lysstråle ved 90 o i visningsretningen. Dette skyldes at røykpartiklene oppdages av reflektert lys og dans på grunn av de millioner av tilfeldige treff fra de raskt bevegelige luftmolekylene. Dette kalles brunisk bevegelse (se nedenfor i væsker). På et hvilket som helst tidspunkt vil treffene ikke være like, slik at røykpartikkelen får en større bashing i en tilfeldig retning. Et togassmolekylediffusjonseksperiment er illustrert ovenfor og forklart nedenfor Et langt glassrør (24 cm diameter) er fylt i den ene enden med en plugg av bomullsull gjennomvåt i konsentrasjon. saltsyre forseglet med en gummibund (for helse og sikkerhet) og røret holdes helt stille, klemmet i horisontal stilling. En lignende plug of conc. ammoniakkoppløsning er plassert i den andre enden. De fuktede bomullspluggene vil avgi røyk av henholdsvis HCl og NH3, og hvis røret blir uforstyrret og horisontalt, til tross for mangel på rørbevegelse, f. eks. NO shaking å blande og fravær av konveksjon, en hvit sky danner ca 1 3 r langs fra konsentrasjonen. saltsyre rør ende. Forklaring: Hva skjer er fargeløse gasser, ammoniakk og hydrogenklorid, diffus ned i røret og reagerer for å danne fine hvite krystaller av salt ammoniumklorid. ammoniakk hydrogenklorid ammoniumklorid NH3 (g) HC1 (g) gt NH 4 Cl (s) Merk regelen: Jo mindre molekylærmasse, desto større er molekylernes gjennomsnittlige hastighet (men alle gasser har samme gjennomsnittlige kinetiske energi ved samme temperatur). Derfor er jo mindre molekylmassen, desto raskere diffunderer gassen. f. eks Mr (NH3) 14 1x3 17. beveger seg raskere enn M r (HCl) 1 35.5 36.5 OG det er derfor de møter nærmere HCl-enden av røret. Så eksperimentet er ikke bare bevis for molekylbevegelse. Det er også bevis på at molekyler med forskjellige molekylmasser beveger seg i forskjellige hastigheter. For en matematisk behandling, se Grahams diffusjonslove. En farget gass, tyngre enn luften (større tetthet), settes inn i bunnen av gassburken, og en andre gassburk med fargeløs luft med lavere tetthet plasseres over den, skilt med et glassdeksel. Diffusjonsforsøk bør vedlegges ved konstant temperatur for å minimere forstyrrelser ved konveksjon. Hvis glassdekselet er fjernet, diffuserer (f) de fargeløse luftgassene ned i den fargede brune gassen og (ii) brom diffunderer opp i luften. Den tilfeldige partikkelbevegelsen som fører til blanding, kan ikke skyldes konveksjon fordi den tettere gasen starter i bunnen. Ingen rysting eller andre former for blanding er nødvendig. Den tilfeldige bevegelsen av begge partiklene er nok til å sikre at begge gassene til slutt blir helt blandet ved diffusjon (spredt til hverandre). Dette er klart bevis for diffusjon på grunn av den tilfeldige kontinuerlige bevegelse av alle gasspartiklene og i utgangspunktet nettbevegelsen av en type partikkel fra en høyere til en lavere konsentrasjon (nedover en diffusjonsgradient). Når det er fullstendig blandet, observeres ingen ytterligere fargeendringsfordeling, men tilfeldig partikkelbevegelse fortsetter. Se også andre bevis i væskeseksjonen etter partikkelmodellen for diffusjonsdiagrammet nedenfor. En partikkelmodell av diffusjon i gasser. Tenk diffusjonsgradienten fra venstre til høyre for de grønne partiklene lagt til de blå partiklene til venstre. For de grønne partiklene er nettomigrasjonen fra venstre til høyre og fortsetter i en lukket beholder til alle partiklene er jevnt fordelt i gassbeholderen (som vist på bildet). Diffusjon er raskere i gasser i forhold til væskesolosjoner fordi det er mer plass mellom partiklene for andre partikler å bevege seg inn i tilfeldig. Når et fast stoff oppvarmes, vibrerer partiklene sterkere ettersom de får kinetisk energi, og partikkelen tiltrekker seg kraftig. Til slutt, ved smeltepunktet. De attraktive kreftene er for svake til å holde partiklene i strukturen sammen på en bestilt måte, og så smelter smeltepunktet. Merk at de intermolekylære kreftene fremdeles er der for å holde bulkvæsken sammen, men effekten er ikke sterk nok til å danne et bestilt krystallgitter av et fast stoff. Partiklene blir frie til å bevege seg rundt og miste deres bestilte arrangement. Energi er nødvendig for å overvinne de attraktive kreftene og gi partiklene økt kinetisk energi av vibrasjon. Så er det tatt varme fra omgivelsene og smelting er en endoterm prosess (916H ve). Energiendringer for disse fysiske endringer i tilstanden for en rekke stoffer behandles i en del av energilevnene. Forklares ved bruk av den kinetiske partikkeltorien om væsker og faste stoffer Ved avkjøling, mister væskepartikler kinetisk energi og kan dermed bli sterkere tiltrukket av hverandre. Når temperaturen er lav nok, er partikkelsens kinetiske energi utilstrekkelig for å forhindre at partikkelen tiltrekker seg krefter som danner et fast stoff. Til slutt ved frysepunktet er tiltrengningskraftene tilstrekkelig til å fjerne eventuell gjenværende bevegelsesfrihet (når det gjelder ett sted til et annet) og partiklene kommer sammen for å danne det bestilte faste arrangementet (selv om partiklene fortsatt har vibrasjons kinetisk energi. må fjernes til omgivelsene, så rart som det kan virke, er frysing en eksoterm prosess (916H ve). Sammenligning av energiforandringer av tilstandsendringer, gass, flytende, solidt 2f (i) Kjølekurve. Hva skjer med temperaturen til et stoff hvis den avkjøles fra gassformen til fast tilstanden Merk temperaturen forblir konstant under tilstandsendringene ved kondensering ved temperatur Tc og frigjøring ved temperatur Tf. Dette skyldes at all varmeenergien fjernet ved avkjøling ved disse temperaturene (latente varmer eller enthalpier av tilstandsendring), muliggjør styrking av interpartikkelkreftene (intermolekylær binding) uten temperaturfall. Varmetapet kompenserer d ved den eksoterme økte intermolekylære krafttiltrengningen. Mellom de horisontale tilstandsendringsseksjonene i grafen kan du se at energifjerningen reduserer partikkelsens kinetiske energi, senker temperaturen på stoffet. Se avsnitt 2. For detaljert beskrivelse av statens endringer. En kjølingskurve oppsummerer endringene: For hver tilstandsendring må energi fjernes. kjent som latent varme. Faktiske energiværdier for disse fysiske endringer av tilstanden for en rekke stoffer blir behandlet mer detaljert i energilevnene. 2f (ii) Oppvarmingskurve. Hva skjer med temperaturen til et stoff hvis det er oppvarmet fra fast tilstand til gassformig tilstand. Merk temperaturen forblir konstant under tilstandsendringer i smelting ved temperatur Tm og kokende ved temperatur Tb. Dette skyldes at all energi som absorberes ved oppvarming ved disse temperaturene (de latente varme eller enthalpier av tilstandsendring), svekkes interpartikkelkreftene (intermolekylær binding) uten temperaturstigning. Varmegjenoppløsningen er den endotermicheatabsorberte energien som kreves for å redusere de intermolekylære krefter . Mellom de horisontale tilstandsendringsseksjonene i grafen kan du se at energiinngangen øker partikelets kinetiske energi og øker temperaturen på stoffet. Se avsnitt 2. For detaljert beskrivelse av statens endringer. En varmekurve oppsummerer endringene: For hver tilstandsendring må energi legges til. kjent som latent varme. Faktiske energiværdier for disse fysiske endringer av tilstanden for en rekke stoffer blir behandlet mer detaljert i energilevnene. SPESIFIKKE LATTE VARMER Den latente varmen for staten endres solid lign væske kalles den spesifikke latente fusjonsvarmen (for smelting eller frysing). The latent heat for the state changes liquid ltgt gas is called the specific latent heat of vaporisation (for condensing, evaporation or boiling) For more on latent heat see my physics notes on specific latent heat Explained using the kinetic particle theory of gases and solids This is when a solid, on heating, directly changes into a gas without melting, AND the gas on cooling reforms a solid directly without condensing to a liquid. Sublimation usually just involves a physical change BUT its not always that simple (see ammonium chloride). Theory in terms of particles . When the solid is heated the particles vibrate with increasing force from the added thermal energy. If the particles have enough kinetic energy of vibration to partially overcome the particleparticle attractive forces you would expect the solid to melt. HOWEVER, if the particles at this point have enough energy at this point that would have led to boiling, the liquid will NOT form and the solid turns directly into a gas. Overall endothermic change . energy absorbed and taken in to the system. On cooling, the particles move slower and have less kinetic energy. Eventually, when the particle kinetic energy is low enough, it will allow the particleparticle attractive forces to produce a liquid. BUT the energy may be low enough to permit direct formation of the solid, i. e. the particles do NOT have enough kinetic energy to maintain a liquid state Overall exothermic change . energy released and given out to the surroundings. Even at room temperature bottles of solid iodine show crystals forming at the top of the bottle above the solid. The warmer the laboratory, the more crystals form when it cools down at night If you gently heat iodine in a test tube you see the iodine readily sublime and recrystallise on the cooler surface near the top of the test tube. The formation of a particular form of frost involves the direct freezing of water vapour (gas). Frost can also evaporate directly back to water vapour (gas) and this happens in the dry and extremely cold winters of the Gobi Desert on a sunny day. H 2 O (s) H 2 O (g) (physical change only) Solid carbon dioxide (dry ice) is formed on cooling the gas down to less than 78 o C. On warming it changes directly to a very cold gas. condensing any water vapour in the air to a mist, hence its use in stage effects. CO 2 (s) CO 2 (g) (physical change only) On heating strongly in a test tube, white solid ammonium chloride . decomposes into a mixture of two colourless gases ammonia and hydrogen chloride. On cooling the reaction is reversed and solid ammonium chloride reforms at the cooler top surface of the test tube. Ammonium chloride heat energy ammonia hydrogen chloride T his involves both chemical and physical changes and is so is more complicated than examples 1. to 3. In fact the ionic ammonium chloride crystals change into covalent ammonia and hydrogen chloride gases which are naturally far more volatile (covalent substances generally have much lower melting and boiling points than ionic substances). The liquid particle picture does not figure here, but the other models fully apply apart from state changes involving liquid formation. GAS particle model and SOLID particle model links. PLEASE NOTE, At a higher level of study . you need to study the gls phase diagram for water and the vapour pressure curve of ice at particular temperatures . For example, if the ambient vapour pressure is less than the equilibrium vapour pressure at the temperature of the ice, sublimation can readily take place. The snow and ice in the colder regions of the Gobi Desert do not melt in the Sun, they just slowly sublimely disappear 2 h. More on the heat changes in physical changes of state Changes of physical state i. e. gas ltgt liquid ltgt solid are also accompanied by energy changes. To melt a solid, or boilevaporate a liquid, heat energy must be absorbed or taken in from the surroundings, so these are endothermic energy changes. The system is heated to effect these changes. To condense a gas, or freeze a solid, heat energy must be removed or given out to the surroundings, so these are exothermic energy changes. The system is cooled to effect these changes. Generally speaking, the greater the forces between the particles, the greater the energy needed to effect the state change AND the higher the melting point and boiling point. A comparison of energy needed to melt or boil different types of substance (This is more for advanced level students) The heat energy change involved in a state change can be expressed in kJmol of substance for a fair comparison. In the table below 916H melt is the energy needed to melt 1 mole of the substance (formula mass in g). 916H vap is the energy needed to vaporise by evaporation or boiling 1 mole of the substance (formula mass in g). For simple small covalent molecules, the energy absorbed by the material is relatively small to melt or vaporise the substance and the bigger the molecule the greater the intermolecular forces. These forces are weak compared to the chemical bonds holding atoms together in a molecule itself. Relatively low energies are needed to melt or vapourise them. These substances have relatively low melting points and boiling points. For strongly bonded 3D networks e. g. (iii) and a metal lattice of ions and free outer electrons ( m etallic bonding ), the structures are much stronger in a continuous way because of the continuous chemical bonding throughout the structure. Consequently, much greater energies are required to melt or vaporise the material. This is why they have so much higher melting points and boiling points. Type of bonding, structure and attractive forces operating Melting point K (Kelvin) o C 273 Energy needed to melt substance Boiling point K (Kelvin) o C 273 Energy needed to boil substance 3a. WHAT HAPPENS TO PARTICLES WHEN A SOLID DISSOLVES IN A LIQUID SOLVENT What do the words SOLVENT, SOLUTE and SOLUTION mean When a solid (the solute ) dissolves in a liquid (the solvent ) the resulting mixture is called a solution . In general: solute solvent gt solution So, the solute is what dissolves in a solvent, a solvent is a liquid that dissolves things and the solution is the result of dissolving something in a solvent. The solid loses all its regular structure and the individual solid particles (molecules or ions) are now completely free from each other and randomly mix with the original liquid particles, and all particles can move around at random. This describes salt dissolving in water, sugar dissolving in tea or wax dissolving in a hydrocarbon solvent like white spirit. It does not usually involve a chemical reaction, so it is generally an example of a physical change . Whatever the changes in volume of the solid liquid, compared to the final solution, the Law of Conservation of Mass still applies. This means: mass of solid solute mass of liquid solvent mass of solution after mixing and dissolving. You cannot create mass or lose mass . but just change the mass of substances into another form. If the solvent is evaporated . then the solid is reformed e. g. if a salt solution is left out for a long time or gently heated to speed things up, eventually salt crystals form, the process is called crystallisation . 3b. WHAT HAPPENS TO PARTICLES WHEN TWO LIQUIDS COMPLETELY MIX WITH EACH OTHER WHAT DOES THE WORD MISCIBLE MEAN Using the particle model to explain miscible liquids. If two liquids completely mix in terms of their particles, they are called miscible liquids because they fully dissolve in each other. This is shown in the diagram below where the particles completely mix and move at random. The process can be reversed by fractional distillation . 3c. WHAT HAPPENS TO PARTICLES WHEN TWO LIQUIDS DO NOT MIX WITH EACH OTHER WHAT DOES THE WORD IMMISCIBLE MEAN WHY DO THE LIQUIDS NOT MIX Using the particle model to explain immiscible liquids. If the two liquids do NOT mix . they form two separate layers and are known as immiscible liquids, illustrated in the diagram below where the lower purple liquid will be more dense than the upper layer of the green liquid. You can separate these two liquids using a separating funnel . The reason for this is that the interaction between the molecules of one of the liquids alone is stronger than the interaction between the two different molecules of the different liquids. For example, the force of attraction between water molecules is much greater than either oiloil molecules or oilwater molecules, so two separate layers form because the water molecules, in terms of energy change, are favoured by sticking together. 3d. How a separating funnel is used 1. The mixture is put in the separating funnel with the stopper on and the tap closed and the layers left to settle out. 2. The stopper is removed, and the tap is opened so that you can carefully run the lower grey layer off first into a beaker. 3. The tap is then closed again, leaving behind the upper yellow layer liquid, so separating the two immiscible liquids. Appendix 1 some SIMPLE particle pictures of ELEMENTS, COMPOUNDS and MIXTURES GCSEIGCSE multiple choice QUIZ on states of matter gases, liquids amp solids Some easy basic exercises from KS3 science QCA 7G quotParticle model of solids, liquids and gasesquot Multiple Choice Questions for Science revision on gases, liquids and solids particle models, properties, explaining the differences between them. See also for gas calculations gcse chemistry revision free detailed notes on states of matter to help revise igcse chemistry igcse chemistry revision notes on states of matter O level chemistry revision free detailed notes on states of matter to help revise gcse chemistry free detailed notes on states of matter to help revise O level chemistry free online website to help revise states of matter for gcse chemistry free online website to help revise states of matter for igcse chemistry free online website to help revise O level states of matter chemistry how to succeed in questions on states of matter for gcse chemistry how to succeed at igcse chemistry how to succeed at O level chemistry a good website for free questions on states of matter to help to pass gcse chemistry questions on states of matter a good website for free help to pass igcse chemistry with revision notes on states of matter a good website for free help to pass O level chemistry what are the three states of matter draw a diagram of the particle model diagram of a gas, particle theory of a gas, draw a particle model diagram of a liquid, particle theory of a liquid, draw a particle model diagram of a solid, particle theory of a solid, what is diffusion why can you have diffusion in gases and liquids but not in solids what are the limitations of the particle model of a gas liquid or solid how to use the particle model to explain the properties of a gas, what causes gas pressure how to use the particle model to explain the properties of a solid, how to use the particle model to explain the properties of a solid, why is a gas easily compressed but difficult to compress a liquid or solid how do we use the particle model to explain changes of state explaining melting with the particle model, explaining boiling with the particle model, explaining evaporation using the particle model, explaining condensing using the particle model, explaining freezing with the particle model, how do you read a thermometer wor king out the state of a substance at a particular temperature given its melting point and boiling point, how to draw a cooling curve, how to draw a heating curve, how to explain heatingcooling curves in terms of state changes and latent heat, what is sublimation what substances sublime explaining endothermic and exothermic energy changes of state, using the particle model to explain miscible and immiscible liquids GASES, LIQUIDS, SOLIDS, States of Matter, particle models, theory of state changes, melting, boiling, evaporation, condensing, freezing, solidifying, cooling curves, 1.1 Three states of matter: 1.1a gases, 1.1b liquids, 1.1c solids 2. State changes: 2a evaporation and boiling, 2b condensation, 2c distillation, 2d melting, 2e freezing, 2f cooling and heating curves and relative energy changes, 2g sublimation 3. Dissolving, solutions. miscibleimmiscible liquids Boiling Boiling point Brownian motion Changes of state Condensing Cooling curve Diffusion Dissolving Evaporation Freezing Freezing point Gas particle picture Heating curve Liquid particle picture Melting Melting point miscibleimmiscible liquids Properties of gases Properties of liquids Properties of solids solutions sublimation Solid particle picture GCSEIGCSE multiple choice QUIZ on states of matter gases liquids solids practice revision questions Revision notes on particle models and properties of gases, liquids and solids KS4 Science GCSEIGCSEO level Chemistry Information on particle models and properties of gases, liquids and solids for revising for AQA GCSE Science, Edexcel Science chemistry IGCSE Chemistry notes on particle models and properties of gases, liquids and solids OCR 21st Century Science, OCR Gateway Science notes on particle models and properties of gases, liquids and solids WJEC gcse science chemistry notes on particl e models and properties of gases, liquids and solids CIE O Level chemistry CIE IGCSE chemistry notes on particle models and properties of gases, liquids and solids CCEACEA gcse science chemistry (revise courses equal to US grade 8, grade 9 grade 10) science chemistry courses revision guides explanation chemical equations for particle models and properties of gases, liquids and solids educational videos on particle models and properties of gases, liquids and solids guidebooks for revising particle models and properties of gases, liquids and solids textbooks on particle models and properties of gases, liquids and solids state changes amp particle model for AQA AS chemistry, state changes amp particle model for Edexcel A level AS chemistry, state changes amp particle model for A level OCR AS chemistry A, state changes amp particle model for OCR Salters AS chemistry B, state changes amp particle model for AQA A level chemistry, state changes amp particle model for A level Edexcel A level c hemistry, state changes amp particle model for OCR A level chemistry A, state changes amp particle model for A level OCR Salters A level chemistry B state changes amp particle model for US Honours grade 11 grade 12 state changes amp particle model for pre-university chemistry courses pre-university A level revision notes for state changes amp particle model A level guide notes on state changes amp particle model for schools colleges academies science course tutors images pictures diagrams for state changes amp particle model A level chemistry revision notes on state changes amp particle model for revising module topics notes to help on understanding of state changes amp particle model university courses in science careers in science jobs in the industry laboratory assistant apprenticeships technical internships USA US grade 11 grade 11 AQA A level chemistry notes on state changes amp particle model Edexcel A level chemistry notes on state changes amp particle model for OCR A level chem istry notes WJEC A level chemistry notes on state changes amp particle model CCEACEA A level chemistry notes on state changes amp particle model for university entrance examinations describe some limitations of the particle model for gases, liquids and solidslight and the eye Sight is the sense organ of radiant energy . It evolved in relation to the materials that absorb, reflect or refract solar radiation. Its sense modality is light . presented in experience as luminance, color and objects in three dimensional space. Since ancient times the eye has been an icon for our consciousness and seeing the metaphor for intelligence 151 and with good biological justification. The order Primates, which includes humans, have in common binocular vision and a greatly expanded visual cortex for the processing of visual information. Vision is a primates dominant sensory domain. The eye is an attractive study for two reasons. It is self contained, which means that all the pieces of the puzzle are found within a single organ. It is also a sublime mechanism, with parts that resemble a camera lens, a daylight filter, an aperture control, and a CMOS160image sensor. However the true organ of vision is not the eye but the brain. By the time it enters awareness . color is really a complex judgment experienced as a sensation . The tissue encapsulated by the eye is an outpost of brain neurons that scan the world and record the basic luminance, contrast and movement in an optical image. The large visual cortex at the back of the brain, in tandem with many other brain areas, does the work of conceptualizing and visualizing a world of colors and objects around us. The visual tasks of image enhancement and interpretation are described in the pages on the structure of vision . This page starts with the physical attributes of light, the optical structure of the eye, the responses of photoreceptor cells to light (including the trichromatic foundation of vision and its unmistakable icon, the chromaticity diagram ), and the specific ways the eye is adapted to meet the visual challenges created by the physical world. light: the spectrum we can see The nuclear fusion occuring within the sun produces a massive flow of radiation into space. Scientists describe this radiation both as cycles or waves in an electromagnetic field and as tiny quantum packets of energy ( photons ). color vision The distance between the peaks in one cycle of an electromagnetic wave is its wavelength (symbol lambda ), measured in nanometers (billionths of a meter). The number of wave peaks within a standard distance is the wavenumber . the reciprocal of wavelength ( 1lambda ), which must be multiplied by 10 million to yield waves per centimeter. Thus, a wavelength of 500160nm equals a wavenumber of 150010 7 or 20,000 waves per centimeter. Light waves increase in frequency (number of cycles per second) as the radiation increases in energy short wavelength, high frequency light has roughly twice the energy of long wavelength, low frequency light. Frequency is a constant property of light at a given energy. When light passes through a transmitting (translucent or transparent) material, the speed of light and the corresponding wavelength of light are reduced somewhat, although the frequency of the light remains unchanged. This produces the characteristic refraction or bending of light as the light waves cross the boundary between different media, such as air and water or air and glass. The ratio between the speed of light in air and its speed through a transmitting medium 151 which determines the amount of bending produced in the light beam 151 is the refractive index of the medium. The baseline wavelength and speed of light are usually measured in air at the earths surface. Describing Light 038 Color. Light is the electromagnetic radiation that stimulates the eye. This stimulation depends on both energy (frequency, expressed as wavelength) and quantity of light (number of photons). the visible electromagnetic spectrum spectrum colors as produced by a diffraction grating ( IR infrared, UV ultraviolet) for a discussion of spectral color reproduction on a computer monitor, see the Rendering Spectra page by Andrew Young The figure shows the visible spectrum on a wavelength scale, roughly as it appears in sunlight reflected from a diffraction grating (such as a compact disc), which produces an equal spacing of light wavelengths. (A rainbow or glass prism produces an equal spacing of wavenumbers, which compresses the blue end of the spectrum.) Outside the visible range, electromagnetic radiation at higher energies (wavelengths shorter than 380 nanometers) is called ultraviolet and includes xrays and gamma rays. Lower energy radiation (at wavelengths longer than about 800160nm) is called infrared or heat at still lower frequencies (longer wavelengths) are microwaves, television waves and radio waves. Notice the very gradual falloff in luminosity at the near infrared (IR) end of the spectrum, and the relatively sharper falloff toward ultraviolet (UV). At the earths surface, the absorbing effects of the the ozone layer and lower atmosphere significantly filter short wavelength radiation below 450160nm and block all radiation below 320160nm. In addition, most wavelengths below 500160nm are blocked from reaching the retina by the transparent yellow tint in the adult lens and a protective yellow pigment layer on the retina. But in noon daylight there is as much energy in long wavelength (heat) radiation as there is in light, so the gradual falloff in perceptible red light is due to weaker visual sensitivity in longer wavelengths. Thus, the range of light wavelengths is somewhat arbitrary. Photometric standards for the visible wavelengths at daylight levels of illumination are from 360160nm at the near ultraviolet end to 830160nm at the near infrared. However under normal viewing conditions, the effective visual limits are between 400160nm to 700160nm . as shown in most diagrams on this site. Yet it is possible to see wavelengths down to 380160nm or up to 900160nm if the light is bright enough or viewed in near darkness. Within the spectrum, the spectral hues do not have clear boundaries, but appear to shade continuously from one hue to the next across color bands of unequal width. It is easier to locate the center of these color categories than the edges the approximate wavelength location of basic color categories (including cyan or blue green) is shown in the figure (above). Note the fairly sharp transitions from blue to cyan and from green to yellow, and the narrow span of cyan and yellow (which can appear white in a rainbow). I use quotation marks to refer to spectral colors because light itself has no color . Color is fundamentally a complex judgment experienced as a sensation . It is not an objective feature of the physical world 151 but it is not an illusion, either. A single wavelength of the spectrum or monochromatic light . seen as an isolated, bright light in a dark surround, creates the perception of a recognizable hue but the same light wavelength can change color if it is viewed in a different context . For example, long wavelength or red light can, in the right setting, appear red, scarlet, crimson, pink, maroon, brown, gray or even black Similarly, in all the diagrams or illustrations of color vision (including the chromaticity diagram ), spectrum colors are only symbols for the different wavelengths of light. Despite all that, the abstract wavelength numbers are conveniently made more interpretable by the use of standard hue categories. Ive summarized below the hue terminology adopted throughout this site. It uses the six primary hue categories red, orange, yellow, green, blue and violet . with blends indicated by compound names in which the first hue is a tint or bias in the second hue: blue violet indicates a violet leaning toward blue. spectral hue categories Note . Hue boundaries rounded to the nearest 10160nm. Spectral hue boundaries are arbitrary, due to the gradual blending of one hue into the next, the shifts in hue boundaries produced by luminance changes, individual differences in color perception, and language variation in the number and meaning of hue categories. c means complement of wavelength for extraspectral hues (mixtures of orange red and blue violet light). Sources . complementary hues from Wyszecki 038 Stiles (1982) hue boundaries from my own CIECAM spectral hue scaling of watercolor pigments, Munsell hue categories and spectral wavelengths. These labels are only guidelines. In addition to the context factors mentioned above, the hue boundaries will appear to shift as the luminance (brightness) of the spectrum increases individual differences in color perception create substantial disagreement in the location of color boundaries, or the location of pure colors such as the unique hues (red, yellow, green and blue) and the location of boundaries will change with the number of hue categories used and the meaning assigned to them (especially across different languages or cultures). Variations in Natural Light. Radiation from the sun that does get through the atmosphere and is visible to our eyes can be described in three ways: 149160 Sunlight is light coming directly from the sun 151 the image of the suns disk or a shaft of sunlight into a darkened room. The solar color changes significantly across the day and depends on the angle of the sun above the horizon, the altitude of the viewer above sea level, the season, the geographical location and the amount of water vapor, dust and smoke in the air. The sun itself is so brilliant that it overwhelms color vision, making color judgments unreliable, but if the noon sun were dimmed sufficiently, its color would appear a pale greenish yellow (not the deep yellow of schoolroom paintings). This color appears in the positive afterimage of sunlight reflected off a car windshield. 149160 Skylight refers to the blue light of the sky as viewed from a location in complete shade, for example the light entering through a north facing window. It results from the scattering of short wavelength light by air molecules. This scattering is slightly stronger from the northern sky, opposite the generally southern origin of sunlight. The illuminance contribution of skylight is significant: though much dimmer than the suns disk, the visible area of the sky is approximately 100,000 times larger, which is why daylight shadows are clearly illuminated and we can read a summer novel in deep shade. 149160 Daylight is the combined light of sun and sky, for example as reflected from an unshaded sheet of white paper illuminated outdoors. Significant color shifts occur in daylight, depending on geography, season and time of day, but it is unchanged by scattered clouds or overcast: these only dim the light and diffuse it. The most accurate way to describe these color changes in natural light is by means of a spectral power distribution (SPD). This is a measurement of the radiance or radiant power (energy per second) of light within a small interval of the spectrum (such as 570-575160nm for wavelengths). Usually the power within each wavelength or wavenumber interval is shown as a proportion of a standard wavelength or maximum power, given an arbitrary value of 100, which creates a relative SPD . Many relative SPDs have been published as standard illuminants . which are spectral templates used to model the characteristics of natural light and to describe artificial light sources and light filters. Two of these, the standard noon daylight illuminant ( D65 ) and noon sunlight illuminant ( D55 ), are shown below, along with the SPDs for north skylight and sunset light. (The numbers associated with the illuminants indicate the closest matching correlated color temperature of the light.) spectral variations in natural light standardized relative spectral power distributions for daylight phases across the visible spectrum, normalized to equal power at 560160nm, with the correlated color temperature (CCT) of each profile (Wyszecki Stiles, 1982) The most interesting of these templates is D65 . the noon daylight illuminant. This SPD is useful in color vision research because it is perceived as a balanced white illumination across a wide range of illumination levels 151 rain or shine, we perceive daylight as white light, provided the sun is not near the horizon. This is the first of many facts that confirm our color vision is not an abstract and impartial color sensor but is a living system that anticipates the range of natural surface colors as they appear under natural illumination . The noon north skylight illuminant is in contrast strongly skewed toward the blue wavelengths, and this in the shade illumination appears distinctly blue to the eye. Noon sunlight ( D55 ) has a nearly flat distribution and appears to be a yellowish or pinkish white when the eye is adapted to noon daylight. When the sun is lower in the sky at sunrise or sunset, sunlight must pass sideways through a much longer and denser section of the earths atmosphere, which scatters most of the blue and green wavelengths to produce a distinctly yellow or red hue. (Sunlight is also reddened by dust storms, ash from volcanic eruptions or the smoke from large fires.) This lends morning or late afternoon light a strong yellow or red bias, climaxing in the deep orange of sunrise or sunset. Morning light has a softer, rosier color, in part because the cooler night air has a higher relative humidity that produces long wavelength filtering morning fogs or mists, and in part because the drop in temperature abates daytime winds and convection currents, allowing dust and smoke to settle out of the atmosphere. Thus, the illumination that reveals our world is not constant but varies across a broad swath of tints from cool blues to warm yellows and reds. The eye is adapted to minimize the distorting effect that these color changes in the light have on the color appearance of objects. Finally, the eye is adapted to function across illumination levels from 0.001 lux (starry night) to more than 100,000 lux (noon daylight), which makes us functional day or night. Moonlight has the same spectral power distribution as daylight, though much reduced in intensity, so the D65 illuminant stands for the daylight and nighttime extremes of natural light experience. However, our color experience of light and objects changes dramatically within that illumination range, as the eye changes from trichromatic photopic vision to monochromatic scotopic vision . design of the eye The eye is a marvel of biological adaptation to a specific function. In large part this adaptation is successful because it separates visual tasks into four levels of structure: the optical eye, the retina, the photoreceptor cells, and the photopigment molecules. 149160 scotopic or dim light adapted rods (denoted by V and containing the photopigment rhodopsin ), most sensitive to green wavelengths at around 505160nm 149160 short wavelength or S 160cones, containing cyanolabe and most sensitive to blue violet wavelengths at around 445160nm. 149160 medium wavelength or M 160cones, containing chlorolabe and most sensitive to green wavelengths at around 540160nm 149160 long wavelength or L 160cones, containing the photopigment erythrolabe and most sensitive to greenish yellow wavelengths at around 565160nm As the figure shows, there is a large number of differences between rhodopsin (taken as baseline) and the S 160photopigment, and a similarly large number of differences between the S 160and M 160photopigments. In contrast, the M 160and L 160photopigments are nearly identical. Photopigments do not catch light particles the way a bucket catches rain. Even if a photon strikes a photopigment molecule, the probability that the visual pigment will photoisomerize depends on the wavelength (energy) of the light . Each photopigment is most likely to react to light at its wavelength of peak sensitivity . Other wavelengths (or frequencies) also cause the photopigment to react, but this is less likely to happen and so requires on average a larger number of photons (greater light intensity) to occur. Measuring Photoreceptor Light Sensitivity. The relationship between photopigment chemistry and light sensitivity was anticipated by 19th century visual researchers, and was demonstrated when the rod photopigment (then called visual purple ) was extracted from dissected retinas and shown to bleach readily in light. Over a century later, methods were developed to measure the bleaching of cone and rod photopigments to specific light wavelengths, which produces a relative sensitivity curve across the spectrum for each type of photopigment or cone. As the curve gets higher, the probability increases that the photopigment will be bleached (and the photoreceptor cell will respond) at that wavelength. The photopigment absorption curves shown below were measured in about 150 intact cones from surgically removed human eyes, held in a tiny glass tube and illuminated from the side by a thin beam of monochromatic (single wavelength) light (a technique called microspectrophotometry ). They closely resemble the recordings of single cones in monkey retinas and the absorption curves of genetically manufactured photopigment molecules. These curves have been normalized 151 the sensitivity at each wavelength is expressed as a proportion of the maximum sensitivity, which is assigned a value of 1.0. human photopigment absorption curves curves normalized to equal peak absorptance (1.0) on a linear vertical scale wavelength of peak absorptance in italics, number of photoreceptors measured for each curve at base of curve data from Dartnall, Bowmaker Mollon (1983) Four kinds of spectra were obtained with four distinct absorptance peaks at 420, 495, 530 and 560160nm. As expected from the photopigment molecular structure . the L 160and M 160photopigments have a similar peak and span within the spectrum, and both differ significantly from the location of the S 160cone curve. The fourth (rod) photopigment, rhodopsin . fits in between. The photoisomerization curves should describe color vision if each type of cone contains only one kind of photopigment and if the intensity of the photoreceptor response is proportional to the quantity of photoisomerized pigment. In fact, these curves do not correspond to human color matching responses, especially for the L160cones . So we have to shift attention to the cones as they respond in an intact (living) retina. It is impractical to measure cone responses in live human retinas, so methods have been contrived since the late 19th century to measure them by indirect methods. Within the past few decades, genetic identification of the specific opsin types expressed in individual photopigments has produced an increasingly accurate picture. The most reliable data on cone sensitivity curves or cone fundamentals actually comes from a different experimental method, also first used in the 19th century: color matching experiments . In this approach, viewers match the color of a test wavelength by a mixture of three primary lights. These matches are performed by normal trichromats and by carefully screened dichromats (colorblind subjects) who lack one of the L . M 160or S 160photopigments entirely or carry L and M photopigments that are very similar . Differences between the dichromats allow measurement of either the L or M light response without any contribution from the other type of cone. These measurements are then used to transform the color matching functions of normal subjects into cone fundamentals that match the separate curves found in dichromats. Adjustments must also be made to compensate for the prereceptoral filtering of short wavelength light by the lens and macular pigment. Alternate techniques, including measurement of nerve signals from individual human cones or rhesus monkey cones, have been used to confirm and clarify the color matching data. Because the cones are unequally distributed across the retina, it matters how large (visual angle) and where (centrally or peripherally) the color stimulus appears in the visual field 151 different presentations of color stimuli will produce different color matching functions. The standard alternatives are a 2deg (foveal) or 10deg (wide field) presentation of color areas centered in the field of view. Compared to 2deg curves, the 10deg L 160and M 160curves are elevated by 10 to 40 in the green to violet wavelengths. For reasons explained here . the 10deg curves are used throughout this site. The cone fundamentals seem to imply that cone sensitivities are fixed, like the speed of a photographic film. They are not: cone sensitivity depends on light intensity . and the curves below describe the average response under moderate levels of retinal illuminance. The absolute level of all sensitivities changes as part of light adaptation . and the relative sensitivities change during chromatic adaptation . Five Views of the Cone Fundamentals. Lets now look at five types of presentation using recent estimates of 10 degree, quantal cone fundamentals by Andrew Stockman and Lindsay Sharpe (2000). 1. Linear Normalized Cone Fundamentals . This is the most common textbook presentation of cone response sensitivities. The response at each wavelength is shown as a proportion of the peak response, which is set equal to 1.0 on a linear vertical scale. This produces the three similar (but not identical) curves shown below. normalized cone sensitivity functions the Stockman 038 Sharpe (2000) 10deg quantal cone fundamentals, normalized to equal peak values of 1.0 on a linear vertical scale This presentation is in some respects misleading, because it distorts the functional relationships between light wavelength (energy), cone sensitivity and color perception. However, comparison with the photopigment absorption curves above identifies three obvious differences between the shape and peak sensitivity of the photopigment and cone fundamentals: 149160The L 160cone has a noticeably broader or wider curve than the S 160and M 160cones the S 160cone has a narrower response profile than either the M 160or L 160cones. 149160Compared to the photopigments, the cone peak sensitivities have been shifted toward long wavelengths . by 5160nm ( L 160cone) to 25160nm ( S 160cone). 149160The short wavelength tails of the photopigment curves have been lowered so that the response below 500160nm falls toward zero. As the effects of prereceptoral filtering have been removed, this implies that increased S 160outputs are opposed to the L and M outputs . at short wavelengths, the S 160cone suppresses the L 160and M 160cone sensitivity. Overall, human spectral sensitivity is split into two parts . a peaked short wavelength sensitivity centered on blue violet (445160nm), and a broad long wavelength sensitivity centered around yellow green ( 560160nm), with a trough of minimum sensitivity in middle blue (475 to 485160nm). 2. Log Normalized Cone Fundamentals . A problem with the linear normalized cone fundamentals is that they emphasize the overall peak shape of the curves as a result they do not adequately display the tails or extreme low values. The solution is to present the normalized curves on a log vertical scale, as shown below. Each unit of the log sensitivity scale is 10 times smaller than the unit before, which zooms in on the very low sensitivities. (Cone fundamentals are most often tablulated in log normalized form, as it is easy to convert these curves into any other format.) log normalized cone sensitivity functions the Stockman 038 Sharpe (2000) 10deg quantal cone fundamentals, normalized to equal peak values of 1.0 on a log vertical scale These curves provide three additional insights: 149160 Each type of cone responds to a wide range of light wavelengths in fact, the measurable sensitivity of the L 160and M 160cones extends over the entire visible spectrum, although the sensitivity of the M 160cone is very low in the near infrared. 149160The L160and M160response curves largely overlap one another 151 and this overlap significantly limits the maximum saturation of hues in the yellow through green wavelengths. 149160The S160cone responds to only half the spectrum . from yellow green to violet perception of monochromatic yellow green to red hues depends entirely on the balance between L 160and M 160outputs. 3. Log Population Weighted Cone Fundamentals . The previous two formats imply that the different photopigments or cone spectral classes are represented in the retina in equal numbers. This is not true, which suggests the cone fundamentals should be weighted (shifted up or down in relation to each other) to more accurately represent their proportional contribution to color vision. The peak values of each cone are set equal to the proportion of that cone in the total number of cones in the retina. The probability that a cone will respond is weighted by the probability that a photon will strike that cone type. The population proportions used here are approximately those of the 10deg retinal anatomy: 63 L 160cones, 31 M 160cones, and 6 S 160cones. (There is reliable evidence that these proportions differ significantly from one person to the next.) population weighted log cone sensitivity functions the Stockman 038 Sharpe (2000) 10deg quantal cone sensitivity functions on a log vertical scale (1.0 total cumulative response by all three cones) area of 50 or more optical density of macular pigment and adult lens shown in yellow from Stockman, Sharpe 038 Fach (1999) Taking into account both the individual response sensitivities of the three cone classes and their proportional numbers in the retina, we see that a random photon of equal energy or white light is most likely to produce a response in an L 160cone at any wavelength above 445160nm. In contrast, the M 160cones have only 40 of the L 160cone response probability across all wavelengths, and the S 160cones only one tenth of that. Thus, a single photon is roughly 25 times more likely to produce a response in an L 160than an S 160cone. 4. Linear Population Weighted Cone Fundamentals . The log scale is useful to show the very low values of cone fundamentals, in the tails of the curve, but it gives an unfamiliar view of the overall shape of the population weighted curves. Represented on a linear scale, the curves reveal the response probabilities more directly. population weighted linear cone sensitivity functions the Stockman 038 Sharpe (2000) 10deg quantal cone fundamentals on a linear vertical scale, scaled to reflect L . M 160and S 160cone proportions in the retina (1.0 total cumulative response by all three cones) This is probably the most accurate picture of the proportional response probabilities of the three cone classes in relation to each other, to different wavelengths of light, and to our overall visual acuity. We glean a few more insights: 149160The L160and M160cones produce nearly all the information acquired by the retina the L 160cones account for most of the retinal signal at nearly all wavelengths. When we recall that the fovea contains half the total number of L 160and M 160cones in the retina, the curves indicate the dominant importance of foveal responses in color vision. 149160The linear scale emphasizes that each cone responds primarily to light near its wavelength of maximum sensitivity (the three white lines in the spectrum band). A single photon at a cones peak sensitivity has a visual impact equivalent to 10,000 or more photons at the tails or low sensitivity ends of the curve. 149160As a result, our eyes are most sensitive to yellow green wavelengths around the middle of the spectrum: yellows and greens are the most luminous colors in a prism spectrum or rainbow. In fact, most of our light sensitivity lies between 500160nm to 620160nm 151 roughly from blue green to scarlet. 149160The sensitivities of the L 160and M 160cones are well contrasted through the red to yellow green parts of the spectrum, but become very similar through the blue green to blue violet parts of the spectrum. The S 160cones break the tie in wavelengths below 5. Equal Area Cone Fundamentals . The population weighted curves are a physiological representation of visual sensitivity: the cones are weighted by their proportional numbers in the retina. But individual cone outputs have unequal importance or voting strength in determining color sensations because they flow into common pathways or channels of color information. These channels have a weight or importance of their own, which defines the perceptual importance of the cone classes in brightness and color perception. A plausible assumption adopted in colorimetry is that each type of cone contributes equally in the perception of a pure white or achromatic color. This means that the cone fundamentals do not represent individual photoreceptors, but classes or types of cones as a group. Each class is given equal perceptual weight in the visual system. In this type of display, the peak of each sensitivity curve is scaled up or down so that the area under each curve (equivalent to the total response sensitivity of each type of cone, pooled across all cones) is the same these curves are usually presented on a linear vertical scale. equal area cone sensitivity functions the Stockman 038 Sharpe (2000) 10deg cone fundamentals rescaled so that the area under each curve equals 10 on a linear scale These equal area cone sensitivity curves have an important and specific technical role in colorimetry . to model the changes in cone sensitivities that occur in each class of cone during chromatic adaptation . This equal area presentation of cone fundamentals should not be confused with the most commonly used model of visual sensitivity based on equal area weighting: the curves of standard color matching functions . These are superficially similar to cone fundamentals, and can be derived from the cone fundamentals by a mathematical transformation, but they do not represent specific photoreceptors or color channels in the visual system. The large differences in peak elevations (especially when compared to the population weighted cone fundamentals) imply that the S 160cone outputs must be heavily weighted in the visual system far out of proportion to their numbers in the retina. This turns out to be true. In addition, the proportionally small overlap between the S 160cone curve and the L 160and M 160curves implies that short wavelength (violet) is handled as a separate chromatic channel and is perceptually the most chromatic or saturated. We might also suspect that the L 160and M 160cones have a different functional role in color vision from the S 160cones, because they have very similar response profiles across the spectrum and lower response weights than the S cones. And this also is true: the L 160and M 160cones are responsible for brightnesslightness perception, provide extreme visual acuity, and respond more quickly to temporal or spatial changes in the image the S 160cones contribute primarily to chromatic (color) perceptions. photopic 038 scotopic vision The separate L . M 160and S 160cone fundamentals do not directly answer a more basic question: what is the eyes overall sensitivity to light How much radiant power must a light emit before we can see it The answer still depends on the wavelength of the light, but it also depends on the total intensity or energy of the illumination 151 the difference between daylight and darkness. Daylight (Photopic) Sensitivity. At illumination levels above 10 lux or so, corresponding to daylight levels of illuminance from twilight to noon daylight, the cones primarily define the luminance or brightness of a light or surface. This is photopic vision . and it is functioning whenever we see two or more different hues. Photopic sensitivity was one of the first visual attributes that 19th century psychophysicists attempted to measure. A plausible early approach was heterochromatic brightness matching . in which viewers adjust the brightness (radiance) of a monochromatic (single wavelength) light until it visually matched the brightness of a white light standard after this was done across the entire spectrum, it yielded a curve of overall light sensitivity. Unfortunately, colored light is not perceived the same as white light: hue purity increases the sensation of brightness . making saturated lights appear brighter than a white light of equal luminance. Various methods have been tried to get around the problem. The most reliable is flicker photometry . which cancels the chromatic component in a monochromatic light by flickering it on and off so rapidly that it appears to fuse into a steady, desaturated, half bright stimulus, which is then adjusted to the white light standard. The diagram shows results from six different measurement techniques, listed in the key in descending order of reliability, to show the extent of the problems. a passel of photopic sensitivity functions luminous efficiency measured using six different techniques (from Wyszecki 038 Stiles, 1982) The underlying problem, it turns out, is not in the measurement but in the theory: the diagram is not a picture of measurement problems but of visual adaptability. The brightness sensation is a dynamic response by different types of photoreceptors adjusting to different visual contexts. Overall light sensitivity varies across different luminance levels . light mixtures and dominant colors it varies depending on how it is measured. So it cannot be pinned down as a single curve, as can be done with the four types of photoreceptors. Even so, the curve is useful in many practical applications. So the international standards body for color measurement methods, the Commission Internationale de lEclairage (or CIE ) cut the Gordion knot and adopted a photopic sensitivity function denoted V ( lambda ), which means a curve of the luminous efficiency value V at each wavelength lambda . This curve was based on early (up to 1924) sets of diverse 2deg color matching functions weighted to reproduce, at the corresponding wavelengths, the apparent brightness of the three rgb primary lights used in the color matching studies. This standard curve locates the main light sensitivity in the green center of the spectrum between 500160nm to 610160nm, and places the peak photopic sensitivity at 555160nm 151 though as you see above, this peak is more of a plateau. The V ( lambda ) luminosity function equivalently represents the relative luminous efficacy of radiant energy, the light stimulating power of equal watts at each wavelength. In this guise it is the basis of modern photometry as deployed in photographic light meters and digital camera image sensors. An electronic sensor measures the radiance within small sections of the visible spectrum, then weights each section by its luminous efficacy the total across the spectrum matches to a good approximation the lights luminance or apparent brightness to the human eye when the light is viewed in isolation. Here is the curve on a log vertical scale, with its partner the scoptopic sensitivity function denoted V ( lambda ) and discussed in the next section. photopic 038 scoptopic sensitivity functions CIE 1951 scotopic luminous efficiency and CIE 1964 wide field (10deg) photopic luminous efficiency, relative to peak photopic sensitivity on log vertical scale relative peak sensitivities from Kaiser Boynton (1996) Unfortunately, photopic sensitivity has remained a moving target. All measurements include the prereceptoral filtering in brightness judgments, which complicates measurement in the blue and violet wavelengths. Subsequent research also showed that the CIE 1924 curve underestimated photopic sensitivity in the blue wavelengths, so the curve has been twice corrected 151 by Judd (1951) and Vos (1978). This modified Judd-Vos luminosity function is usually denoted V M ( lambda ) 151 M 160for modified . Meanwhile a consensus emerged that the S 160cones do not contribute substantially to brightness perception. This means the photopic luminosity function is more accurately defined as a weighted combination of the L 160and M 160 cone sensitivity curves . Paradoxically, when more realistic corrections for lens and macular density are added, these newer estimates increase even further the estimated photopic sensitivity to short wavelength light, despite exclusion of the S 160cone from the curve. The diagram below presents the updated 2deg luminosity function denoted V ( lambda ) and the companion 10deg luminosity function by Stockman 038 Sharpe, normalized on a linear scale. The modified 1978 Judd-Vos curve ( V M lambda ) and the 1951 scotopic curve V ( lambda ) are included for comparison. The new curves are based on the Stockman 038 Sharpe L 160and M 160cone fundamentals that best fit flicker photometric data for 40 viewers the L cones have a 50 greater weight than the M 160cones and the S 160cones are given zero weight. These curves put the peak photopic sensitivity at 545160nm, but with a flattened peak due to the averaged values of variant L 160photopigments . photopic 038 scoptopic luminosity functions photopic functions based on the 2deg and 10deg quantal cone fundamentals of Sharpe, Stockman, Jagla 038 Jaumlgle (2005), shown with the CIE 1951 scotopic function and the Judd-Vos 1978 photopic function all curves normalized to equal peak sensitivity on a linear vertical scale These curves show that short wavelength or blue light has a greater luminous efficiency under scotopic than photopic vision. They show that differences among the photopic curves are confined almost entirely to the short wavelengths, and that there is a greater blue response in wide field than foveal color perception. Finally, they show that long wavelength or red light strongly stimulates the photopic function but the scotopic very little. This is why submariners and astronomers dark adapt under red light: it keeps the foveal cones functional (for detail vision) while dark adapting the rods. Both cones and rods respond near the maximum to green wavelengths, regardless of luminance. This is why emergency response vehicles are now painted a light yellow green instead of the traditional red 151 the yellow green is much easier to see, especially in dim light. Dim Light (Scotopic) Sensitivity. The diagrams above also show the CIE 1951 scotopic sensitivity function denoted V ( lambda ) which describes human light sensitivity under dark adaptation at illuminances below 0.1 lux. This is approximately the amount of light available under a half moon at night. At these very low illuminance levels the cones cannot respond to light and the rods completely define our visual experience. There are seven peculiarities of rod based or scotopic vision: 149160All rods contain the same photopigment, rhodopsin, so rods lack the photopigment variety necessary for color vision. We become functionally colorblind except for isolated points of higher luminance, such as distant traffic lights or the planet Mars, that are bright enough to stimulate the cones. 149160Rod signals do not transmit within separate nerve pathways: they feed into the same channels used by the cones. These channels are segregated into contrasting redgreen and yellowblue opponent contrasts . As a result, rods can produce faint color sensations 151 at very low chroma and lightness contrast. 149160 Peak sensitivity is around 505160nm or blue green. As natural light around sunset is shifted toward red, the rods start to dark adapt while still exposed to long wavelength (red) light. 149160However, rod sensations of white usually appear faint blue (matching about 480160nm) and not blue green. 149160There are roughly 100 million rods in the human retina, yet they are completely absent from the fovea at the center of the visual field where daylight visual resolution is highest. We cannot read even large print text under scotopic vision, or recognize very small objects, because the fovea shuts down. 149160There are about 16 rods for every cone in the eye, but there are only about 1 million separate nerve pathways from each eye to the brain. This means that the average pathway must carry information from 6 cones and 100 rods This pooling of so many rod outputs in a single signal considerably reduces scotopic visual resolution and means, despite their huge numbers, that rod visual acuity is only about 120th that of the cones. 149160Like the cones, the rods are more widely spaced and larger in diameter toward the edges of the retina, but they also form a densely packed ring at about a 20deg visual angle around the fovea. This is why we can see very faint stars or lights at night if we look to one side, rather than directly at, their location. Mesopic Light Sensitivity. The rods strongly affect color perception under moderately low illumination by mixing with or tinting the color responses of the still active cones. This mesopic vision typically appears in illuminances from 0.1 to 10 lux, for example during the 45 minutes or so after sunset (for a viewer outdoors and shielded from artificial light). Because the rod and cone outputs are pooled in shared nerve pathways in mesopic vision, the photopic luminosity curve shifts toward blue and long wavelength hues become darker. Bright yellow, ochre and umber fuse into a single grayish tan, greens and blues appear as a single grue (green blue) color, and reds become a warm, dark gray. This Purkinje shift (named for the Bohemian scientist who described it in 1825) is easiest to see in large areas of color extending outside the visual field of the rodless fovea. It is quite noticeable if you look at a familiar, brightly colored art print, hawaiian shirt or flower bed in fading twilight as your eyes become adapted to the dark. In daylight illumination the rod signals are near maximum, which causes a ceiling effect that makes the rods insensitive to light contrast. (This is due to a response compression of the rod outputs, and not to photopigment depletion by light.) The rod signals therefore disappear in the same way cone outputs do in a ganzfeld effect . Even so, rods remain active in daylight, even under very bright levels of illuminance. They can affect color appearance by a process called rod intrusion . which desaturates colors, especially at long (red) wavelengths, in large field or peripheral vision, and under moderate to low levels of illumination. The Color Vision Research Laboratories at UC San Diego provide a comprehensive online library of data relating to photopigments, cone fundamentals, colorimetry and visual responses. trichromatic mixtures The premise that millions of distinct colors can arise from the stimulation of three different color receptors is called the three color or trichromatic theory of color vision, first proposed in the 18th century. It is the foundation of modern colorimetry . the prediction of perceived color matches from the physical measurement of lights or surfaces. The cone sensitivity curves show the probability that individual L . M 160or S 160cones will respond to light at different wavelengths. But they do not offer a very clear picture of how the cones work together or how the mind triangulates from the separate cone outputs to identify specific colors. We obtain this picture by charting the proportion of cone outputs in the perception of a specific color. This results in a literal triangle, the trilinear mixing triangle . that contains all possible colors of light. Any diagram that shows how the L . M 160and S 160cones combine to create color perceptions must also define a specific geometry of color . This geometry changes, depending on how the cone signals are combined. The relationships among cone outputs, the method for calculating the outputs that produce a specific color sensation, and the shape of color in the mind, are all aspects of the same problem. Principle of Univariance. A key feature of photoreceptor signals is that they represent light as a contrast or change to a continuous baseline signal of about 15040 millivolts, even in darkness (hence the name dark current ). A change in photoreceptor excitation is transmitted as a more or less change in this baseline signal. This single type of photoreceptor response to any and all light stimulation is termed the principle of univariance . Now, the rate of photoisomerization in the photopigment depends on two completely separate dimensions of the light stimulus: (1)160the quantity of light incident on the retina or (2)160the relative sensitivity of the photopigment to the light wavelength(s). As a result, a change in the photoreceptor signal can be caused by two very different changes in the light. The cone or rod output decreases as the light gets brighter or as the light frequency gets closer to the frequency of its peak sensitivity and the output increases as the light becomes dimmer or farther from its peak sensitivity. the principle of univariance a single L cone responds with the same more or less signals to changes in light frequency or light intensity Thus there are two kinds of ambiguity in the response of individual photoreceptors to light (diagram, above): 149160 A single type of cone cannot distinguish changes in wavelength (hue) from changes in radiance (intensity) . Alternating between equally bright green and red wavelengths ( B ), or modulating a single green wavelength of light between bright and dim ( C ), will produce an identical change in the output of a solitary L cone. 149160 Some changes in light produce no cone response . Alternating between equally bright blue and orange wavelengths ( A ), or between a dim green and proportionately bright red light ( D ), would not change the output of that solitary L cone. However, what the cones cannot do individually they can achieve as a team. The principle of univariance means that color must be defined by the combined response of all three cone types . The Cone Excitation Space. To visualize the color creating relationships among the separate L . M 160and S 160cones, they are used to define a three dimensional space. In this cone excitation space each dimension represents the separate and independent excitation or outputs produced in each type of cone. The standard method to illustrate cone behavior is to combine the three cone responses produced by monochromatic lights from short (390160nm) to long (750160nm) wavelengths. This is done by plotting the cone fundamentals at each wavelength as points in the cone excitation space. For example (diagram, right), at a wavelength of 500160nm, the L cone sensitivity is 0.44, M is 0.64 and S is 0.09. Those three numbers locate the combined cone excitation to monochromatic light at 500160nm. When similar points are plotted for all visible wavelengths, they define a curved path of cone excitations to monochromatic (maximally saturated) lights called the spectrum locus . a normalized cone excitation space the spectrum locus (red dots) plotted in three dimensions defined by the normalized cone fundamentals L . M and S V is the photopic luminous efficiency function We still can recognize in this curve the basic features of the normalized L . M and S cone fundamentals. All points at wavelengths below 400160nm or above 700160nm are at the origin (0 on all dimensions) which means those wavelengths are invisible 151 they produce no cone excitations. The L cone reaches its maximum response at around 565160nm, the M cone at around 540160nm, and the S cone at around 445160nm. But now we see them in dynamic combination. The V luminosity function (green line in diagram) is the sum LM of the normalized L and M outputs, so it forms a diagonal from the origin and in the L, M plane. The contrast between the L and M outputs ( L150M ) forms the opposing diagonal. We can also find the location of any complex color, if we know the cone excitations it produces. The white point ( wp ) produced by an equal energy illuminant is found as the total area under each cone fundamental divided by the sum of all three fundamental areas: L 0.44, M 0.37, and S 0.19. The extraspectral mixtures of red and violet extend as a line between the red and violet lights used to mix them 151 in the diagram, between 620160nm and 445160nm. reading cone responses to a 500160nm monochromatic light If we turn this diagram to look at it sideways, we see that the boundary of color space is geometrically irregular . No simple geometrical shape can describe the spectrum locus. It forms a roughly elliptical outline when viewed from one side (diagram, right) but a double lobed or pinched shape when viewed along the luminance diagonal (diagram, above). This double lobed shape reappears in the spectrum locus of color models, such as CIELAB or CIECAM . that contrast colors with a white surface. This double lobed shape occurs because the spectrum locus is bent at a 90deg angle along a line from the origin to approximately 525160nm (middle green, purple line in diagrams above and right). The vertical half, comprising all wavelengths below 525160nm that produce a significant S cone response, sticks upward like a shark fin. The rest of the spectrum locus 151 wavelengths above 525160nm where the S cone response is effectively zero 151 lies completely flat on the L, M plane. As a result of this bend, the color space is inherently curved . For example, mixing the wavelengths 575160nm and 475160nm in the right proportions will produce a white light. Therefore the mixing line between them must pass through the achromatic white point: but this can only be done with a curve (diagram, right). Moreover, the shape of this curve changes as we mix different pairs of complementary wavelengths. The curvature of chromaticity plane stretched inside the closed spectrum locus is geometrically irregular, too. The diagram demonstrates how the L and M cones operate in tandem to define luminance. For lights below 525160nm, luminance is defined by the projection of the spectrum locus into the L, M plane (dotted line in diagram, right). But if we set aside luminance perception defined by the LM diagonal, then color perception is divided into two parts : 149160at wavelengths above 525160nm . changes in the relative excitation of the L and M cones define the color response the S cones are silent. 149160at wavelengths below 525160nm . the relative L, M excitations are approximately the same as they are at 525160nm (the dotted line and purple line are equivalent) so it is the relative excitation of the independent S cone that defines the color response. This two part geometry is the photoreceptor foundation for the opponent geometry of color appearance. A final observation is that the white point is not located on the luminosity function. This simply demonstrates that white is not the same as bright . The perception of white is a form of color sensation, whereas the perception of bright is a unique intensity sensation. The cone excitation space implies that a bright stimulus produces more than two times the cone excitation of a white surface, and therefore visual white always has a lower luminosity than visual bright under the same viewing conditions. The Chromaticity Plane. Reweighting the cone fundamentals, for example by doubling the M cone response or by using equal area or population weighted cone fundamentals, changes the relative length of the dimensions but does not alter the fundamentally curved and irregular geometry of the cone excitation space. 160 However, we get a radically different color space through a different approach. By removing variations in the brightness of different wavelengths, we flatten the curvature of the three dimensional spectrum locus. This is done by normalizing on the total cone excitation, or dividing the excitation in each cone by the stimulation produced in all cones: If we divide the excitation produced in each cone type ( L c . M c and S c ) by this amount, we get the relative proportion of the color sensation that is separately contributed by each of the three cone types. This is the chromaticity of the color: The previous example only described a single wavelength of light, so we simply sum the cone excitations at that single blue green wavelength: 1600.64 0.44 0.09 side view of the cone excitation space This procedure radically transforms the color space in two ways (diagram, right): (1) it uncouples the red and violet ends of the spectrum locus, which were previously joined at the origin (zero values) because they are both very dark hues (2) it projects the spectrum locus onto the plane surface of an equilateral triangle (blue) whose corners are located at the three maximum values for the three cones. The three dimensional spectrum locus has been flattened into two dimensions, and the original banana shaped color space has been transformed into something resembling a right triangle. If we define the L . M and S dimensions as the response each cone relative to its maximum response, then a line from the origin to the white point ( wp ) forms an achromatic gray scale. It is customary to display this transformed spectrum locus so that the triangle plane is perpendicular to view. In this orientation it forms a trilinear mixing triangle or a Maxwell triangle . after the 19th century English physicist James Clerk Maxwell who first used it. The trilinear mixing triangle does not represent differences in brightness or lightness between colors, only differences in chromaticity (hue and hue purity). Chromaticity is the color in color, separate from its lightness or brightness. For this reason, the area within the mixing triangle that is enclosed by the bowed spectrum locus (and a line connecting the extreme short and long wavelengths) is called a chromaticity diagram . This figure offers many fundamental insights into the geometry of color and is worth patient study. a trilinear mixing triangle and chromaticity diagram any possible combination of three cone outputs can be represented as a unique point within the triangle the range of physically possible colors is contained inside the spectrum locus 149160Each corner of the triangle represents the color that would be perceived by the maximum excitation of a single L . M 160or S 160cone without any excitation in the other two cones. The sides of the triangle represent shared excitations between just two cone types, with no contribution from the third. Any location inside the triangle represents a color that results from the stimulation of all three types of cone. 149160The mixture proportions for each cone are shown along the triangle sides. By definition every trilinear mixture must sum to 100, so a mixture of 50 S 160and 38 L 160(color a ) must contain 12160 M (by subtraction: 1001505015038 12). Therefore just two chromaticity values uniquely specify every color in a chromaticity diagram. 149160The point where all three primaries contribute in proportions equal to their perceptual weight is the white point . The white point changes its location within the chromaticity diagram depending on how the three cone outputs are weighted the diagram shows them weighted proportional to the areas under the normalized cone fundamentals (44, 37, 19). 149160The chromaticities of monochromatic (single wavelength) lights define the spectrum locus . the trace of the most intense colors physically possible. The line of red and blue mixtures between 400160nm and 700160nm, which includes magenta and purple, is called the purple line . 149160As explained above . spectral hues at wavelengths above 525160nm are defined only by the relative proportion of L and M outputs they lie on the straight line LM base of the equilateral triangle. Hues below 525160nm are produced by a roughly constant ratio of L and M outputs, so are distinguished only by the relative percentage of S cone excitation. 149160All mixtures of two real colors of light (such as colors a and b ) define a straight mixing line across the chromaticity space. All colors produced by the mixture of those two colors of light must lie along the mixing line. 149160The hue purity or chroma of a color is defined as the length of the mixing line between the color and the white point. It is obvious that monochromatic hues do not have equal hue purity: spectral yellow appears rather pale or whitish because it is close to the white point, and spectral violet has the highest chroma because it is far away. 149160All mixtures outside the spectrum locus and purple line are cone proportions that cannot be produced by any physical light or surface. They are physically impossible or unrealizable colors . This gray area shows that about half of the unique combinations of cone outputs cannot be produced by any physical stimulus . It also shows that these colors 151 especially green primary 151 would appear more saturated than any spectral light. This has nothing to do with the purity of light: it is due to the overlap in cone fundamentals across the spectrum (especially between the L 160and M 160cones), and to the random, side by side mixture of L . M 160and S 160cones within the retina. As a result any light that stimulates one cone also stimulates one or both remaining types of cones. We are physiologically prevented from seeing a pure cone output, and therefore we never see a pure primary color . 149160Very large color differences can be produced by very small differences in cone outputs . For example, the change from white to pure yellow occurs with a change in L 160and S 160cone outputs of less than 20 all green mixtures are produced by changes of less than 30 in the L 160and M 160cone outputs. 149160The chromaticity distance between unique green ( 500160nm) and unique blue ( 450160nm) is extremely large and represents almost the entire range of S 160cone outputs. For this reason the appearance and measurement of blue hues are sensitive to the location of the white point and are variable across different color models . color space defined as cone excitations as a proportion of total cone excitations (brightness) 149160A color appearance does not reveal the cone proportions that created it. In every green color the M 160cone outputs are less than 60 of the total all possible colors contain at least 10 of the L 160outputs most of the possible cone output combinations result in various flavors of blue. 149160Finally, chromaticity diagrams are highly sensitive to assumptions made about how cones combine or are weighted in perception, or how the dimensions are rotated to present the chromaticity diagram to view. The two examples at right show the CIE Yxy chromaticity diagram (top) that has long been a standard in colorimetry but does not describe color differences accurately (for example, it makes green the most saturated spectral hue and gives it the largest perceptual area) and the CIE 1976 UCS chromaticity diagram (bottom), in which the measurement dimensions have been manipulated to represent, as accurately as feasible in a two dimensional diagram, the relative saturation of spectral hues (as their distance from the white point) and the perceptual difference between two similar colors as the chromaticity distance between them in the diagram. 10deg (wide field) and 2deg (foveal) chromaticity diagrams The diagram above shows the change in the chromaticity diagram that occurs if cone fundamentals are weighted so that the area under each curve represents the cone populations for a 10deg retinal area (which includes 6 or more S 160cones) or a 2deg retinal area (which includes less than 1 S 160cones). The foveal weighting produces a substantial reduction in the blue response range and shifts the white point almost to the L150M border. When using a chromaticity diagram, keep in mind that it has mathematically and rather mechanically removed the perceptual effect of brightness. Because the luminance of a red or violet monochromatic or single wavelength light appears quite dim in comparison to a green light, when all lights are the same radiant intensity, the red and violet lights would have to be substantially increased in power to produce a perceptual match to the chromaticity diagram. A chromaticity diagram therefore does not accurately describe, for example, the perception of relative color intensity in a solar spectrum, where the visible wavelengths have roughly similar radiance . The interactive tutorial on color perception hosted by the Brown University Computer Science Department includes a java applet that models the additive mixture of three primary colors. constraints on color vision To conclude this page, lets consider how our visual capabilities are adapted to perception of radiant energy in the world. By comparing our visual capabilities to those of other animals, we can understand how we benefit from three cones, rather than two or four, and why our cones are tuned to specific wavelengths and not others. variety in chromaticity diagrams (top) CIE Yxy diagram, with the xyz primaries rotated to match a maxwell triangle (bottom) CIE UCS diagram, with a primary triangle imputed Standard Assumptions. An assumption made in most studies of animal vision is that photopigment absorption curves conform to a common shape, for example Dartnalls standard shape (right), which is plotted around the pigments peak value on a wavenumber scale. This common shape arises from the backbone opsin molecule structure. Variations in the opsin amino acid sequence only shift the wavenumber of peak sensitivity up or down the spectrum this does not change the basic shape of the curve, though it becomes slightly broader in longer wavelengths. (We have already seen this template similarity in the human photopigment curves .) It is also assumed that each class of photoreceptor contains only one kind of photopigment, and that the principle of univariance describes the photopigments response to light. These three assumptions allow a basic understanding of animal visual systems without painstaking measurement of photopigment or cone response curves. Dartnalls standard shape does not adequately describe human color vision, especially the L160photopigment absorptance, but idealized curves are adequate to illustrate the important constraints on color vision. Monochromatic Vision. The rudimentary form of vision requires a single receptor cell ( V ). For maximum sensitivity this receptor should respond to wavelengths somewhere in the 300160nm to 1000160nm area of the spectrum where solar radiance at the earths surface is most intense. This kind of visual system, which is common in lower vertebrates . codes light along a single luminosity dimension that can only distinguish light from dark. Monochromatic vision can include a mechanism for light adaptation that allows the eye to function across large changes in overall illumination, and it can detect movement, shapes, surface textures and depth. But it cannot easily distinguish between the emitted brightness of lights and the reflected lightness of surfaces, or objects from near or similarly reflecting backgrounds. It also cannot perceive color: changes in hue 151 from green toward either red or blue 151 will appear as luminance changes from light to dark. Nevertheless, all vertebrates have at least this basic visual capability, which suggests that luminance variations are the dominant visual information available from the environment. Humans experience monochromatic vision at night, under scotopic or dark adapted vision when only a single type of photoreceptor (the rods) is active, and under monochromatic illumination such as the red light lamps used by astronomers. a single cone visual system response curve of human rods with maximum sensitivity at 505160nm As only one receptor is involved, the key constraint has to do with the receptor sensitivity peak and breadth within the span of solar radiation. For purely technical reasons the peak solar radiation seems to shift in a range between roughly 500160nm to 900160nm, depending on whether the radiation is summed within wavelength or frequency intervals, and is measured as energy or photon counts and the noon sunlight curve is rather flat throughout this range. So the solar peak is a poor criterion for comparison. Instead we can consider a window of atmospheric transparency or minimum light filtering as measured at the earths surface, which provides a stable frame of reference. dartnalls standard shape expressed on a wavelength scale at a peak value of 505160nm The major causes of light absorption or scattering in our atmosphere are air molecules (including the ozone layer), dust or smoke, and water vapor. As the diagrams at right show, there is an especially close correspondence between the human visual span and the wavelengths of minimum water absorptance . including liquid and water vapor 151 and the large bead of mostly water, the vitreous humor, that inflates the eye and sits between the pupil and retina. Human light sensitivity is located on the uphill side of this lowest point, away from UV radiation and toward the infrared side of the light window. All vertebrates have inherited visual pigments that evolved in fishes, which may explain why our pigments are tuned to these wavelengths. A second possible constraint is the range of chemical variation in photopigments . for example as expressed in all known animal photopigments. The figure below shows the wavelengths of maximum sensitivity for the four human photopigments in relation to animal photopigments with the lowest and highest peak sensitivities 151 from 350160nm (in some birds and insects) to 630160nm (in some fish). This puts the outer boundaries of animal light sensitivity between 300160nm to 800160nm. Human vision is in the middle of the range that other animals have found useful. human visual pigments within span of known animal visual pigments A third constraint has to do with the span of visual pigment sensitivity, because the sensitivity curves must overlap to create the triangulation of color. For Dartnalls standard shape at 50 absorptance, this implies a spacing (peak to peak) of roughly 100160nm. If we include the tail responses at either end of the spectrum, a three cone system could cover a wavelength span of about 400160nm. The fourth and last constraint is more subtle but equally important: avoiding useless or harmful radiation . 149160At wavelengths below 500160nm (near UV), electromagnetic energy becomes potent enough to destroy photopigment molecules and, within a decade or so, to yellow the eyes lens. Many birds and insects have receptors sensitive to UV wavelengths, but these animals have relatively short life spans and die before UV damage becomes significant. Large mammals, in contrast, live longer and accumulate a greater exposure to UV radiation, so their eyes must adapt to filter out or compensate for the damaging effects of UV light. In humans these adaptations include the continual regeneration of receptor cells and the prereceptoral filtering of UV light by the lens and macular pigment. 149160At the other extreme, wavelengths above 800160nm are heat, which is less informative about daylight object attributes: it is dimmer than shorter wavelengths, is heavily absorbed by liquid water or water vapor, and lacks the nuanced spectral variations that can be interpreted as color. In mammals, the visual systems heat sensitivity would have to be shielded from the animals own body heat at wavelengths longer than 1400160nm, and the very long photopigment molecules (or artificial dyes) necessary to absorb radiation in wavelengths between 800160nm to 1400160nm are known to oxidize or decompose readily. These complications make long wavelength energy more trouble than it is worth. On balance, then, it seems that animal vision is limited at the wavelength extremes as much as it is anchored by a radiance peak or an inherited range of photopigment possibilities. Dichromatic Vision. How do animals utilize this limited span of light Many mammals are equipped with a two cone photopic visual system: one cone shifted into the yellow green wavelengths, the other shifted toward the blue end of the spectrum, with substantial overlap between the two sensitivity curves in the green middle. These Y and B cones make up what John Mollon calls the old color system . They enable the eye to distinguish between light radiating in the long versus short wavelengths. light within the absorptance spectrum of water (from Segelstein, 1981) 160 human luminous efficiency and the transmission curve of pure water, by depth (from Soffer 038 Lynch, 1999) A two cone system can distinguish differences in wavelength patterns from total luminance, which means hue can be perceived separate from lightness . The efficient way to do this is to combine the two cone responses to determine a brightness quantity, but to difference or subtract the cone outputs to define a hue contrast (diagram, right). That is, the sum YB creates a supercone that has the same univariant response to hue as the V cone, while the difference Y150B contrasts stimulation at opposite ends of the light spectrum. The difference output is called an opponent coding of the separate cone outputs. It is difficult to overstate the importance of opponent responses in color vision, beginning with the opponent dimensions important to hue sensation but including many other contrast mechanisms discussed in a later page . Primates have retained the backbone of this mammalian vision as the yb opponent function (diagram, below). This opponent function is created from the outputs of two separate cone systems, which requires a bimodal shape in the overall visual response, with a sensitivity peak in the short and long wavelengths (diagram, right). The white point of this function, where the Y ( LM ) and B outputs are equal, is located around 485 to 495160nm (cyan). Like the yellow point that marks equal outputs from L and M cone sensitivity curves, this cyan white marks the point of equal outputs from the Y and B color receptors. Again like yellow, cyan light has a relatively low hue purity and tinting strength compared to the blue or red spectrum extremes. Unlike yellow, however, cyan is visually dimmer than the yellow green response peak of the V cone because the S cones do not significantly contribute to luminance perception. a two cone visual system the human yb opponent (contrast) function with peak sensitivities at 445 and 560160nm, a white point at 495160nm and macular masking of blue response This contrast between short and long wavelength light persists in human color vision as the warmcool color contrast . This is the most general chromatic contrast in color perception, and it appears to have a strong influence on the development and use of color terms in almost all languages. What determines the placement of the two peak sensitivities J.160Lythgoe and J. Partridge demonstrated that a two cone visual system adapted to the green leaves, twigs and brown soil litter of forest habitats gets the greatest chromatic contrast when the peak sensitivities are located between 420160nm to 450160nm ( B ) and 510160nm to 580160nm ( Y ). These ranges include the peak sensitivities of the primate yb opponent function shown above, and primates evolved in forest habitats. Metamerism 038 Colorblindness . There are two important limitations to a visual system based on two partly overlapping sensitivity curves. The first is that very different distributions of light wavelengths will be perceived as the same color, and this occurs among both chromatic (colored) and achromatic (white) color sensations. This problem is called metamerism. Dissimilar spectral distributions that produce the same color sensation are called metamers . A two cone system is especially susceptible to metameric confusions. Metamers occur whenever the two cones are stimulated in the same relative proportions . The most glaring examples include colors perceived as white, when the cone stimulations are 50:50. As the spectral reflectance curves below illustrate, this can occur in reflectance patterns that appear as dissimilar as gray, green or magenta in trichromatic vision. metamers for white (or gray) in a two cone visual system spectral reflectance curves for gray (top), magenta (middle) or green (bottom) would appear indistinguishable in a two cone visual system Parallel problems occur whenever surface color differences produce similar proportional responses in the cones 151 for example, between greens and reds, or purples and blues 151 or when the illumination changes color without changing proportional cone responses. These greatly expand the possible metameric confusions. These problems characterize human dichromatic vision or colorblindness in which typically either the L 160or M 160cones are absent. These folks see an unusually large number of material metamers in the everyday world, and large color differences often appear to them quite subtle. Dichromats are easily confused by yellows and browns, or by blue greens and purples, especially across surfaces of similar lightness. Yellow loses its characteristic lightness, and they commonly see an achromatic or white color in the spectrum located at the cyan balance point between 490160nm to 500160nm. The second limitation in a two cone system is that perception of saturation or hue intensity cannot be easily disentangled from lightness. There are only two possible combinations of two cone outputs: adding them together to define brightness, or contrasting them to define hue. There is no third combination to uniquely define saturation. Despite that, some studies show that human dichromats do see saturation differences, especially at the spectrum ends, but with only half the acuity of trichromats. To do this, the visual system probably uses lightness contrast to estimate chroma, by comparing the lightness of a surface to the lightness of the brightest surface in view. A process called lightness induction performs this contrast judgment in human trichromatic vision. This is how we can see the difference in a achromatic surface between a dark (gray) color and a dimly lit (white) color in red to yellow green surface colors, where S 160cone response can be effectively zero, the same contrast causes surfaces to appear dark (brown) rather than dimly lit (orange). (This is explained further in the section on unsaturated color zones .) separating luminance from hue responses in two cones defined as the sum and difference of the L and M outputs bimodal human visual response based on the Smith 038 Pokorny normalized cone fundamentals A two cone system seems optimally defined to provide a new function 151 chromatic adaptation to the shifts in daylight phases of natural light, from the slightly blue, cool light of noon to the ruddy, warm light of sunset. These changes in lighting significantly shift the apparent hue of surface colors: around sunset a white surface will appear yellow or orange. In human trichromats and dichromats alike, the separate cone sensitivities can be adjusted to increase the B response to compensate for the reduced blue light, and decrease the Y (trichromatic LM ) response to compensate for the increased red light (right), which should restore the white point to its accustomed location. However, color perception in dichromats is significantly affected by luminance contrast 151 dichromats perceive colors of light to grow redder as they get dimmer. This goes in the opposite direction to a compensatory increased sensitivity of the Y receptors, and probably complicates the perception of warm surface colors across changes in the intensity or chromaticity of the illumination. Trichromatic Vision. Finally, all primates 151 monkeys, apes and humans 151 acquired a second set of contrasting receptor cells: the L 160and M 160cones, which evolved from a genetic alteration in the mammalian Y cone. There is only a small difference between the L 160and M 160cones in molecular structure and overlapping spectral absorptance curves . but it is enough to create what Mollon calls the new color system . This defines hue contrasts between middle wavelength (green) light and long wavelength (red) light. These cells are also linked in a contrast or opponent relationship that defines the rg opponent function . a second two cone visual system the human rg opponent (contrast) function with peak sensitivities at 530 and 610160nm, a white point at 575160nm and macular masking of blue response The main benefit of trichromacy is that it creates a unique combination of cone responses for each spectral wavelength and unambiguous hue perception . This enhances object recognition when surfaces are similar in lightness or are randomly shadowed, as under foliage. It also substantially improves the ability to separate the color of light from the color of surfaces, because illuminant metamerism is also reduced color constancy is greatly improved. spectral contrast between direct sunlight and indirect (blue sky) light (from Wyszecki Stiles, 1982) A second important trichromatic benefit is that it reduces metameric colors to various flavors of gray around the white point and into dull blues and purples (diagram at right). As a result the number of physical metameric matches is radically reduced, as anyone who has tried to match household paint colors has found out. In fact, excluding trivial variations, there are no possible metameric emittance profiles under an equal energy white light source for any color at moderate to high saturation. In effect, saturation is a kind of perceptual confidence that hue accurately symbolizes the spectral composition of a color. Near grays, besides generating a very large number of metameric surface colors, are also most susceptible to color change by subtractive mixture with the light source color 151 change the emittance profile of the light, and the surface color changes as well. Metamers that appear identical under noon daylight often scatter into visually different colors under late afternoon light (or interior incandescent light) as the white point shifts from blue to yellow, and this chromaticity scatter is typically elongated in the red to green direction discriminated by the rg contrast (diagram at right). This is a particular problem for automotive manufacturers, who must choose different plastic, fabric and paint materials to get a color match and identical color changes across different phases of natural light . chromaticity of metameric colors in light mixtures and the scatter of illuminant shifted achromatic metamers (from Wyszecki Stiles, 1982) What explains the location of the rg opponent balance or white point at around 575160nm (yellow) This is the approximate spectral direction of both the chromaticity shifts in natural daylight and the approximate hue of the prereceptoral filters . As a result, changes in the angle of sunlight from morning to late afternoon, and the gradual darkening of the lens across age, produce no perceptible change the rg contrast and hence no color change that cannot be handled by adaptation of the yb balance. By the time sunlight acquires a golden or deep yellow appearance it has begun to shift off the yb axis toward red: the rg balance then registers a change and surface colors show the tint of the light. Another intriguing explanation for this yellow balance point appears in the reflectance curves of 1270 color samples from the Munsell Book of Color . The curves at right show 10 colors of identical saturation and value, equally spaced around the hue circle. All the curves seem to inflect in a small region centered on 575160nm which means comparative information about the reflectance curves is minimal at that point. This rg balance point is insensitive to chromaticity for the same reason that a lever is not imbalanced by weight placed over the fulcrum. Placing the yellow balance point at an area of minimal reflectance information makes color vision maximally sensitive to relative green and red changes in surface colors, and permits hue resolution into the red end of the spectrum, where the S 160cones provide no response, as the relative proportion of L 160and M 160response. Why Not 4 or More Cones The final query is: why dont we have four or more cones Why stop with only three reflectance curves for standard Munsell hue samples at constant lightness and saturation from Kuehni (2003) We can exclude the possibility that the obstacle is evolution of new photopigments. Molecular genetics has identified 10 variations in the human L 160and M 160photopigments, which create two clusters of similar peak responses around 530160nm and 555160nm (right). Males are also split roughly 5050 by a single amino acid polymorphism (serine for alanine) that shifts the peak sensitivity in 5 of these variants, including the normal male L 160photopigment, by about 4160nm. Finally, it is genetically possible for about 50 of females to express a fourth red photopigment and some individuals carry genes for only one type of L 160and M 160photopigment while others carry multiple (different) versions. These many combinations can significantly affect trichromatic responses or cause colorblindness . However it is still assumed that cones contain only one kind of photopigment or that cones with chemically similar photopigments output to common nerve pathways. Thus, cones and nerve pathways are the fundamental units of trichromatic vision . not the photopigments. There are twelve unique ways to sum or contrast three cone outputs to define hue: our vision uses six contrasts . plus a single luminance sum. This requires a unique nerve pathway for seven different signals similar outputs in a four cone system would require at least 15 contrast and luminance pathways. There are roughly one million nerve tracts from the eye to the brain, and each tract carries information from roughly six cones and 100 rods. This suggests nerve pathways are a resource that must be conserved. A four channel chromatic system would, at minimum, double this load, grossly decreasing the granularity in the retinal information or requiring an increase in neural processing in the retina and bandwidth in the optic nerve. Evolution could arrive at a more complex visual system, but it would require modifying a visual cortex specialized to receive and interpret the three cone outputs adding a fourth cone would mean reengineering the brain as well. These costs far outweigh any adaptive advantage that four cones could produce. Why 3 Badly Spaced Cones Evolutionary considerations lead to a more basic question: is color really what our visual system is adapted to perceive From a design perspective, the most interesting question is not why we have three rather than four cones, but why the three cone fundamentals are so unevenly spaced along the spectrum and unequally represented (63 L . 31 M 160and 6 S ) in the retina. Our acuity to differences in color (hue and saturation) would substantially improve, and our visible spectrum would significantly expand, if the cone sensitivity curves were more evenly spaced and the retinal cone proportions were better balanced. multiple L 160and M 160photopigments identified in the human retina curves from Backhaus, Kliegl 038 Werner (1998) peak wavelengths from Merbs 038 Nathans (1992) lines connect serinealanine polymorphisms The answer appears in an important optical problem that arises when a large eye is made sensitive to a wide span of the spectrum: chromatic aberration . When light passes through a lens, blue wavelengths are refracted (bent) more strongly than red wavelengths, causing the blue image to focus at a point in front of the red image (diagram at right). This causes overlapping, fuzzy colored fringes in a focused image, especially around the edges of intricate light and dark patterns, such as branches and leaves seen against the sky (right). Chromatic aberration seriously degrades visual acuity, as does a related optical problem, spherical aberration, caused by the somewhat round exterior of the cornea. Manufactured optical instruments solve this problem with a sandwich of lenses, the simplest consisting of a convex and concave doublet, one cancelling the chromatic aberration of the other. Animal lenses are always convex (bulging), and an achromatic doublet requires a rather long focal length (proportionally much longer than the diameter of an eye), so the doublet solution is not feasible in a large eye. However, the red wavelengths require less optical bending to come into focus, which means yellow light requires less precise optics . especially in bright daylight, when the aperture of the eye is small relative to its focal length and the eye essentially becomes a pinhole camera. Evolution tackled chromatic aberration not with complex lenses but with several new adaptations, some of them unique, that substantially reduce the effects of blue and violet wavelengths in the fovea and the eye as a whole: 149160A cornea that is more spherical at its center than around its circumference, reducing spherical aberration at the edges. 149160A cornea, lens and eye diameter (focal length) that produce the most precise image in the yellow wavelengths, where optical demands are less extreme. 149160The prereceptoral filtering in the lens and macular pigment, and in the yellow tint of bleached photopigment, which combine to filter out more than half the blue and violet light below 470160nm. 149160A strong directional sensitivity to light incident on the fovea (the Stiles Crawford effect ), created by the uniform alignment of photopigment in the outer segment discs this causes the photopigment to react less strongly to light coming from the side, which is predominantly scattered blue wavelengths. 149160An overwhelming population (roughly 94) of L 160and M 160receptors, and a close spacing between their sensitivity peaks, which limits the requirement for precise focusing to the yellow green wavelengths. 149160A sparse representation by S 160receptors in the eye (6 of total), which substantially reduces their contribution to spatial contrast, and the nearly complete elimination of S 160cones from the fovea, where sharp focus is critical. 149160Separation of luminosity (contrast) information and color information into separate neural channels, to minimize the impact of color on contrast quality. 149160Neural filtering of signals by the L 160and M 160cones within in the fovea that suppresses color information in detailed, contrasty textures. 149160Neural filtering higher in the visual system to eliminate chromatic aberration from conscious visual experience, and which can (after a period of adjustment) even eliminate blurring that is artificially induced by distorting prisms or eyeglasses. These many adaptations enable the fovea to be extremely effective at edge discrimination . even in strong contrasts of light and dark they also enhance image clarity when the eyes are stereoscopically combined, greatly improving depth perception. Minimizing chromatic aberration has profound benefits for modern humans, as it makes possible the crisp pattern recognition we require to read text, or the acute depth perception necessary to aim weapons or catch a prey. But what about early primates They were small bodied tree dwellers, who had to read the outlines of tree limbs intertwined in space and judge how far to leap to catch the branch of escape or the bough of dangling food. You can see this capability in the amazing fearlessness with which all primates scramble and leap across large distances between tree limbs high above the ground, where a single misjudgment can cause crippling injury or death. Those are stakes that evolution can latch onto. There is a minor downside to a strong selective pressure toward visual acuity and lack of selective pressure toward color discrimination: colorblindness . Because the genes for both the L 160and M 160photopigments are located next to each other on the X chromosome, the lack of duplicate opsin genes in XY males causes frequent variations in the L 160and M 160photopigments that make them chemically similar or identical 151 and can make the 25160nm separation between them disappear. The result is various forms of dichromacy that affect about 5 of the population, nearly all of them males. This red green colorblindness is caused either by missing L 160cones ( protanopia . in 2 of males) or M 160cones ( deuteranopia . in 6 of males). (Lack of S 160cones or tritanopia occurs in less than 0.01 of the population.) These conditions can be diagnosed using very simple perceptual tests, such as the Ishihara color disks . Remarkably, many men do not discover (are not told) that they are colorblind until their teenage years, which strongly suggests yet again that hue discrimination is not essential for most life tasks . (For more on color vision deficiencies, see this page .) chromatic aberration in a simple lens red and green light are focused far behind blue light 160 chromatic aberration and life among the trees A currently popular evolutionary explanation for L150M discrimination is that it assists the detection of red fruit among green foliage, the cherries in the leaves hypothesis (photos, right). But it can also be interpreted as a chromatic contrast designed to minimize the effects of chromatic aberration around a yellow balance point, so that red and green darken equally around the yellow focus. Edge detection and depth perception based on patterns in light and dark has taken evolutionary priority over any problems involving hue discrimination, and it is on these visual stimuli that culture, social consensus and communication really depend. A telling illustration comes in a map of the busiest areas of the human brain: the integrating connections between the visual and language areas. a map of the busiest areas of the human brain after Hagmann P, Cammoun L, Gigandet X, Meuli R, Honey CJ, et al. (2008) We find this edge and pattern imperative carried into our art and documents 151 etchings, woodcuts, monochrome wash and charcoal or pen drawings, printed text, fabric patterns and vegetable weaves 151 all art that appeals entirely to the eyes monochrome perception of pattern and line. Nor is this a matter of simple drawings from simple tools. Even with all our printing and reproduction technologies, text and engineering drawings still exclude varied colors to increase the legibility and interpretability of the document. As we say: to see means to understand, and to understand means to see clearly, not colorfully. The fundamental reference for all things luminous, chromatic and colorimetric is Color Science: Concepts and Methods, Quantitative Data and Formul230 (2nd edition) by Guumlnter Wyszecki and W. S. Stiles (John Wiley: 1982), nearly encyclopedic but showing its age. The best overview of color vision that I have seen 151 compact, informative and up to date, though emphasizing basic perceptual processes and colorimetry 151 is The Science of Color (2nd edition) edited by Steven Shevell (Optical Society of America, 2003). Im especially partial to the overview of experimental methods and evidence in Human160Color Vision (2nd edition) by Peter Kaiser and Robert Boynton (Optical Society of America, 1994). Peter Kaiser also has authored a lucid web site on The Joys of Vision . Color Vision: Perspectives from Different Disciplines (de Grutyer, 1998), edited by Werner Backhaus, Reinhold Kliegl John Werner contains a variety of interesting chapters, including a study of Monets aging eyes. The premier review of color and color vision as it relates to printing, photography and analog video is The Reproduction of Colour (6th ed.) by R. W.G. Hunt (John Wiley: 2004). Introduction to Color Imaging Science by Hsien-Che Lee (Cambridge University Press: 2005) is actually an in depth discussion of color topics relevant to color imaging technologies, including digital imaging. A text with similar topical coverage as Hunt but less formal theory is Billmeyer and Saltzmans Principles of Color Technology (3rd ed.) by Roy S. Berns (Wiley Interscience: 2000). Seeing the Light: Optics in Nature, Photography, Color, Vision and Holography by David Falk, Dieter Brill 038 David Stork (John Wiley: 1986) is an eclectic but very pragmatic and well illustrated traversal of almost every known color phenomenon relevant to modern imaging technologies. Color for Science, Art and Technology edited by Kurt Nassau (North Holland: 1997) is a miscellany of rather unusual chapters on color, such as The Fifteen Causes of Color, Color in Abstract Painting, Organic and Inorganic Pigments, and The Biological and Therapeutic Effects of Light. A short, conversational introduction to color, with emphasis on the issues vexing to cognitive theories, is C. L. Hardins Color for Philosophers: Unweaving the Rainbow (Hackett, 1988). A smattering of interesting essays, including John Mollons chapter old and new color subsystems, is available in Color: Art and Science . edited by Trevor Lamb and Janine Bourriau (Cambridge University Press, 1995.) To remedy the misperception that visual processes are well understood and uncontroversial, see for example James Fultons web site on the Processes of Animal Vision . Last revised 08.I.2015 149 copy 2015 Bruce MacEvoy cherries and life among the trees