gernot hoffmann newton’s prism experiment and goethe’s

�

Gernot Hoffmann

Newton’s Prism Experimentand Goethe’s Objections

Contents �. Introduction 2 2. Snell’slawandSellmeier’sequation 6 3. Calculationsfortheraypath 7 4. Geometryformaximaldispersion 8 5. Rayvisualizationandaphoto 9 6. GamutlimitationforsRGB �0 7. Gamutcompression �� 8. Mappingtherays �2 9. Singleray/RGBclipping �3�0. Singleray/CIELabcompression �4��. Singleray/Linearspectrum �5�2. Multipleray/IlluminantEqualEnergy �6�3. Multipleray/IlluminantsA,D50,D65,D75 �7�4. Goethe’sexplanations �8�5. Conclusions �9�6. Hoffmann’sprismexperiment 20�7. Reverseproblemandinverseappearance 2��8. Thecolorsofdarkness 22�9. Anaturalrainbow 2420. References 25

2

1.1 Introduction / How to use this doc

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3

1.2 Introduction / About Newton

Isaac Newtonlivedfrom�642to�727.HisworkaboutopticsandcolorwasprobablyinspiredbyDescartes,Charleton,BoyleandHook[5].Refractionanddispersionbyprismswerealreadyknownatthistime,butNewtonintroduced�666asetofthreecrucial experiments(infactbynumerousexperiments):

�.Refractionanddispersionofathinray,whichproducesaspectrumbandwithallrainbowcolors:red,orange,yellow,green,blue,indigoandviolet.

2. Condensationofthespectrumbandbyalens.Thisdeliversagainwhitelight.

3. Aspectralcolor,hereasmallpartof thespectrumband,canbe refractedagainbut itcannotbefurtherdispersed.

Indigowasadded-thoughnotvisible-inordertogeta‘harmonic’sequenceliketheseventonesc,d,e,f,g,a,h,(c).Thelast tonechasdoublethefrequencyof thefirst. It isastrangecoincidencethatthisratioisapproximatelyvalidforthefrequenciesorwavelengthsofvisiblelight.Incomputergraphicswehaveastrongcyanbetweengreenandblue.Inprismcolorsitissometimesdetectable-abettercandidatethanindigofortheseventhrainbowcolor.

Newton’stheorieswerebynomeansalwaysclearandunderstandable,whichleadtolengthyandoftenratherimpolitediscussionsbetweenthemostfamousscientistsinEurope.Itissafetosay:Newtonhaddiscoveredthatwhitelightconsistsofcoloredlight.Newtonarrangedthespectrumonacircle.Drawingbytheauthor,basedonaprintinOpticks[�].Connectingtheendsofaspectrumlikethisdoesnothave an equivalent for general electromagnetic oracousticalwaves.Thisdiscoverywasthefirststeptowardssphericalorcylindricalthree-dimensionalcolorspaces[7],[24].Asegmentofthecircleisoccupiedbyviolet.Newton’svioletiscomplementarytoyellow-green.Inourpresentunderstandingthisismainlythemagentasegment,butmagentaismixedbyredandblue(violet)andnotaspectralcolor.

26

YellowOrange

Red

Viole

t

Indigo

Blew

Green

C

DE

F

GA

B

O

Z

Newtonsays:’ThatifthepointZfallinorneartothelineOD,themainingredientsbeingtheredandviolet,theColourcompoundedshallnotbeanyoftheprismatickColours,butapurple,incliningtoredorviolet,accordinglyasthepointZliethonthesideofthelineDOtowardsEortowardsC,andingeneralthecompoundedvioletismorebrightandmorefierythantheuncompounded’.

Newtonknewalreadyadditivecolormixing.Heappliedthecenter of gravity rule (whichisac-curatelyvalidintheCIEchromaticitydiagram)inhiswheel.Zissuchamixture.

ThedifferentrefractionindicesfordifferentwavelengthsleadNewtontotheconclusionthattelescopeswithmirrorsinsteadoflens’shouldbemoreaccurate.Hemanufacturedsuchatelescope,usingametallicsphericalmirror.Theaccuracywasprobablyaffectedbysphericalaberration.Atthattimeitwasassumedthatanidealmirrorshouldhavetheshapeofaconesectionbutitwasnotyetdiscoveredwhichone-aparabola.Manufacturingsuchamirrorwouldhavebeenimpossible.

Newtonpublished ’Opticks’�704,nearly fortyyearsafterhisfirstexperiments. In thetimebetweenhehadspentmuchtimedevelopingmathematicalmethods,geometryandprinciplesofmechanics.

4

Johann Wolfgang von Goethelivedfrom�749to�832.Wellknownaspoetandwriter,hewasfamiliaraswellwithphilosophyandnaturalscience.

�8�0hepublishedhisbookGeschichte der Farbenlehre[2].ThisismainlyahistoricalreviewbutalsoafuriousattackagainstNewton’stheories.Judgingbyouractualunderstandingofnaturalscience,Goethe’scolortheorywasbynomeanswellfoundedandelaborated.Ontheotherhandhetriedtointegratetheaspectsofcultureandartinhisgeneralizingconcepts.

Thequestionremains:whydidGoethenotbelieveintheObviousinNewton’stheories?

Itisthepurposeofthisdocumenttodemonstratethattheobviousinourpresentunderstan-dingwasbynomeansobviousforGoethe.Thisdemonstrationwillbedoneinanengineeringstyle,basedonmanyillustrations.Theseareaccurateinthesenseofclassicalopticsandinthesenseofactualcolortheory.

TheauthorfoundduringhisGooglesearchnearlynowherecorrectillustrationsfortheprismexperiment.Drawingsinpublicationsareoftenwrong[5],[6],thiscouldbealonglist...Oneofthebestillustrationsisthetitlegraphic,dated�9�2[8],butevenhererulesfantasyoverreality:theblue-ishpartistoosmall,indigoisinrealitynotperceivableandthegeometricalpathoftheredrayisnotaccurate.

1.3 Introduction / About Goethe

5

1.4 Introduction / Goethe says...

SomestatementsbyGoethe,importantinourcontext,maybequoted[2],followedbyasim-plifiedtranslation.

A [2,Zweiter Teil, Konfession des Verfassers ]Aberwieverwundertwarich,alsdiedurchsPrismaangeschauteweißeWandnachwievorweißblieb,daßnurda,woeinDunklesdranstieß,sicheinemehroderwenigerentschiedeneFarbezeigte,daßzuletztdieFensterstäbeamallerlebhaftestenfarbigerschienen,indessenamlichtgrauenHimmeldraußenkeineSpurvonFärbungzusehenwar.EsbedurftekeinerlangenÜberlegung,soerkannteich,daßeineGrenzenotwendigsei,umFarbenhervorzu-bringen,undichsprachwiedurcheinenInstinktsogleichvormichlautaus,daßdieNewto-nischeLehrefalschsei.’

’HowsurprisedwasIwhenIlookedthroughaprismontoawhitewall-stillwhite,andcolorsappearedonlytherewheredarkmetwhite.Itwasimmediatelyclearthatcolorscanappearonlyatboundaries.AndIsaidloud,guidedbyaninstinct:Newton’steachingiswrong.’

B[2,Zweiter Teil, Polemischer Teil ]’Also,umbeimRefraktionsfallezuverweilen,aufwelchemsichdieNewtonischeTheoriedocheigentlichgründet,soisteskeineswegsdieBrechungallein,welchedieFarbenerscheinungverursacht;vielmehrbleibteinezweiteBedingungunerläßlich,daßnämlichdieBrechungaufeinBildwirkeundeinsolchesvonderStellewegrücke.EinBildentstehtnurdurchseineGrenzen;unddieseGrenzenübersiehtNewtonganz,jaerleugnetihrenEinfluß...undkeinesBildesMittewirdfarbig,alsinsoferndiefarbigenRändersichberührenoderübergreifen.’

’Againabouttherefraction,whichisthetruebasisofNewton’stheory:coloreffectsarenotgeneratedbyrefractionalone.Asecondnecessaryconditionis, thatrefractionactsonanimagebyshiftingit.Animageiscreatedmerelybyitsboundaries,andtheseboundariesarenottakenintoaccountbyNewton...andnoimagewillbecome colorful in the middle, unlessbecomecolorfulinthemiddle,unlessthecoloredboundariestouchoroverlapeachother.’

C[2,Zweiter Teil, Beiträge zur Optik ]’Unterdeneigentlichen farbigenErscheinungensindnurzwei,dieunseinenganz reinenBegriffgeben,nämlichGelbundBlau.SiehabendiebesondereEigenschaft,daßsiezusam-meneinedritteFarbehervorbringen,diewirGrünnennen.DagegenkennenwirdieroteFarbenieineinemganzreinenZustande:dennwirfinden,daßsiesichentwederzumGelbenoderzumBlauenhinneigt.’

’Onlytwocolorscanbeconsideredaspure:yellowandblue.Theirspecialfeatureis:theygeneratetogetheranewcolorwhichwecallgreen.Redisneverpure:wefindthatthiscolortendseithertoyellowortoblue.’

6

Glass BK7B1 1.039612B2 0.231792B3 1.010469C1 0.006001C2 0.020018C3 103.560653

Glass SF15B1 1.539259B2 0.247621B3 1.038164C1 0.011931C2 0.055608C3 116.416755

0.3 0.4 0.5 0.6 0.7 0.81.50

1.55

1.60

1.65

1.70

1.75

1.80

λ µ/ m

n

BK7

SF15

Therefractionofaraywhichentersfromamediumwithrefractionindexn�intoamediumwithrefractionindexn2isdefinedbySnell’slaw.Theanglesαandβareshownonthenextpage.

Therefractionindexforairispracticallyn�=�.0 and with n�.0andwithn2= nweget:

2. Snell’s law and Sellmeier’s equation

sinsin

nn n

( )( )βα

= =1

2

1

Goethesaid:Willebrord Snellius (�59�–�626)knewthefundamentalsbuthedidnotknow

thedefinitionbysinefunctions[2,Erster Teil, Fünfte Abteilung ].

nB

C

B

C

B

C2 1

2

21

22

22

32

23

1( )λ λλ

λλ

λλ

= +−

+−

+−

ThestructureofthisfunctionisessentiallybasedonMaxwell’stheoryofcontinua[4].Thefunctionhasthreepoleswhichareoutsidethespectrumofvisiblelight.Thepolesindicateresonancephenomenawithoutdamping.Inrealitythepeaksarefinitebecauseofdamping.Theactualparametersarefoundbymeasurements,hereforspecialtypesofflintandcrownglass.Therefractionofflintglassisstronger.Becauseofthesteeperslopethedispersionisstrongeraswell.Combinationsofflintglassandcrownglasscanbeusedforachromaticlensorprismsystemswhichshownodispersionfortwodistinctwavelengthsandnearlynodispersionsfortheothers.Goetheknewthisalready.

TablesaresuppliedbySchottAG [�5],hereusedforflintglassSF�5.Thanksto Danny Rich.TheSellmeierequationandthedataforcrownglassBK7werefoundatWikipedia[�6].

TherefractionindexcanbemodelledasafunctionofthewavelengthbySellmeier’sequation:

7

n 1.5500rho1 45.0000rho2 45.0000alf1 75.0000bet1 38.5486alf2 34.5311bet2 21.4514defl 49.5311

g

C� C2u� u2

d�

d2d0

R2

R�

x

y

g� g2

r� r2

α�

α2

β� β2

n2

n�

P�P2

3. Calculations for the ray path

g

u

d

1

111

11

= −+

= −−

= +

sin

sin

( )cos( )

( )cos( )cos(

γγ

ρρ

ρ ))( )−

= += +==

− =

sinu

g

ρ

λµ

µ λµ

1

1 1 1

1 1 1

2 1

1 2

1 1 1

1

r c ux r dx gx x

g d rxx x x

y y y

x y

d rg d r

dA d g

− =− =

=

λµ λ

1 1

1 1 1

1 1

Solution by Cramer's rule−−

= −

=== +

d gdM d r d r

dM dA

y x

x y y x

1 1

1 1 1 1

1 1

1 1

µµ

α γ ρ

/p g

Refraction by SSnell's lawsin n sin

sina

( ) ( / ) ( )

cos( ) ( )tan

β α

β ββ

1 1

12

1

1

1

12

=

= −= [[ ( ),cos( )]sin β β

δ γ β1 1

1 1= −

g

d

x p dx

2

011

1 1 0

= ++

= ++

= +

sin

sin

( )cos( )cos( )

( )

γγ

δδ

λ

22 2

0 2 0 2

0 1 0 1

2 2

2

== −

= −

== +

µ

β γ δ

g

p g

dA d g d gdM d p d p

dM dA

si

x y y x

x y y x

( / )

nn n sin

sina sin

( ) ( )

cos( ) ( )tan [ ( ),cos( )]

α β

α αα α α

2 2

22

2

2 2 2

12

=

= −=

uu

d

222

2 2

222

= +−

= −

= ++

sin

sin

( )cos( )

cos( )( )

ρρ

δ α γδδ

xx p dx c us p c

1 2 2

2 2 2

2 2 2

2 2 2 2

2 2 2 2

= += += −= −

= −

λµ

dA d u d udM d s d s

x y y x

x y y xx

dM dAr c u2 2 2= + ( / )

Thepathoftherayiscalculatedbyintersectionsoflinesegments,usingSnell’slawandsomesimplegeometry:linesinparametricrepresentation;solutionsbyCramer’srule.Alldirectionvectorsarenormalizedforunitlength.Theoriginofu�isatC�.

8

Glass BK7LBlue 0.3800LRed 0.7000nBlue 1.5337nRed 1.5131

rho1 20.0000rho2 20.0000

For bluealf1 50.0000bet1 29.9643alf2 50.1478bet2 30.0357defl 40.1478

disp 1.8184


rho1 52.0000rho2 0.0000


disp 1.5672

Glass SF15LBlue 0.3800LRed 0.7000nBlue 1.7548nRed 1.6890

rho1 31.4000rho2 31.0000


disp 7.1119


rho1 55.0000rho2 19.0000


disp 5.7646


rho1 19.0000rho2 55.0000


disp 15.4286

4. Geometry for maximal dispersion

Forapracticalprismexperimentthedispersionshouldbeaslargeaspossible.Flintglassisthebetterchoice.Theoptimalanglescanbefoundbytrialanderror.Thesimulationbelowconfirmsthetestresults.Leftcrownglass,rightflintglass.Theuppertwoimagesshowthesymmetricalcase.Thelowershowtheoptimalcase.Theoutputangleβ2shouldbenearto90°fortheshortestwavelength(violet).Inthemiddleimagesonecanseethatlargeinputanglesα�donotdeliverthebestresults.

Crownglass Flintglass


rho1 1.0000rho2 55.0000


disp 6.4668

9

5. Ray visualization and a photo


rho1 19.0000rho2 54.0000For bluealf1 49.0000bet1 25.4729alf2 84.0482bet2 34.5271defl 73.0482

disp 15.4286

Weareusingthroughoutthedocumentwavelengthsfrom0.380µmto0.700µm.Thisrangereachesfromalmostinvisibleviolettoalmostinvisiblered.Thecolorsattheendofthespectrumcanbemadevisibleonlybyratherstronglightsourcesinlaboratories,0.360µmto0.800µm.

AcrudecolorvisualizationapproximationisachievedbynonlinearHSB,amodificationofthestandardHue-Saturation-Brightnessmodel,whichisrepresentedbyacone[9],[24].

Thisisaphotoofarealspectrumbar.Alittleimageprocessingwasapplied.

�0

6. Gamut limitation for sRGB

380460

470475

480

485

490

495

500

505

510

515520 525

530535

540545

550

555

560

565

570

575

580

585590

595600

605610

620635

700

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

x

y

0.65

0.�5

0.25

0.350.450.55

0.05

0.95

0.750.85

Acorrectvisualizationofthecalculatedspectrumbarwouldrequiremediawhichcanreproduceallspectralcolors.Thisisnotpossible,notevenbylasers.Especiallyoneneedsaplausiblecolorreproductiononcommoncathoderaytubemonitors(CRTmonitors).

ThechromaticitydiagramCIExyYbelowisaspecialperspectiveprojectionofthephysicalcolorspaceCIEXYZontoaplane.Thearea,filledsymbolicallybycolors, represents thehumangamut,buttheluminanceisleftout.Spectralcolorsareonthehorseshoecontour.Themagentaline(purpleline)showsmixturesofvioletandred.Magentaitselfisnotaspec-tralcolor.Themagentalineispracticallyafictionbecausetheendpointsarenearlyinvisibleinreallife.Practicalmagentasaremixedbyblueandred.

InsidethehorseshoecontouristhegamuttriangleforsRGB(Rec.709primariesandD65whitepoint),butthistriangleistheprojectionofanaffinedistortedcube.Thegamutdependsontheluminanceaswell,whichisshownforincreasingluminancesY=0.05to0.95[22],[23].

sRGBisastandardizedcolorspace,areasonablemodel forrealCRTmonitors.MappingspectralcolorstosRGBisobviouslyverydifficult.Especiallyvibrantorangesaremissing.

Magentaline(purpleline)

��

7.3 Gamut compression Type C by RGB clippingCrudeRGBclipping-evenproportionalclippinglikehere-doesnotdeliverpleasantresults.

7.2 Gamut compression Type B for multiple ray spectra in CIELabThecompletecompressionasaboveisnotusefulforspectrawhicharegeneratedbyseveralrays.Inthiscasethelightinthemiddleismoreorlesswhiteandanincreasedsaturationwouldbewrong.TheLabluminanceissimplymultipliedbyafactorofabout0.95andonlythefirststepofthecompressionisexecuted.

If R then RIf G then GIf B then Bm R G BIf m

< =< =< ==

0 00 00 0max( , , )

>>

===

1 ThenbeginR R mG G mB B mend

///

7. Gamut compression

Find the hue in Lab by a,b (asterisks L*.. omitted)Reduce thhe radius towards the L-axis until R,G,Bare in-gamutThis ddelivers a ,b ,LModify L by

Reduce the

1 1 1

L L2 0 5 0 7 0 5= +. . ( - . ) radius towards the L-axis until R,G,B

are in-gamutThis deelivers a ,b ,LApply a linear interpolation between 1 an

2 2 2dd 2 and

find the position with maximal saturation

s a b= +2 2 / LLThe gamut compression will be improved later

7.1 Gamut compression Type A for single ray spectra in CIELab

a

b

L

Ifthespectrumisgeneratedbyoneray,thenthevisualizationbysRGBrequiresoptimallysaturatedcolorsandacertainvisualbalanceaswell.Ifanorangecannotbeshownbrightly,thenitislessconvenienttoshowyellowintheneigh-bourhoodasbrightaspossible.Thebluepartlooksalwaystoobright.Thiswell-knownphenomenonwillbeexplainedlater.

Thegamutcompression isdone inCIELab[�0],[2�]by theauthor’ssimplemethod.Moresubtlestrategiesforgamutcompressionsaredescribede.g.byJánMorovicin[�4].

�2

8. Mapping the rays

TheupperimageshowsagainthecrudecolorapproximationbynonlinearHSB,nowwithasmallernumberofcolorrays.Thelowerimageshowsthecontentofanarraywith�000+�elementsonthescreen(rightplane),startingapproximatelyattheorigin.Eachcolorrayhitsanelementofthisarray.Thewavelengthiswrittenintothearray.Gapsarefilledbylinearinterpolation.AtpositionRwehavemanycolorraysperlength,atpositionVfewer.Inordertodistributetheenergycorrectlyacrossthelength,thearraycontentismultipliedbyaslopefactor.ThisiscalculatedbyalinearinterpolationoftheslopesbetweensVandsR.ThecontentofthearrayisconvertedintothecolorspaceCIEXYZ,usingthecommoncolor-matchingfunctions,andthenconvertedtosRGB[�0],[2�],[22].CompressionisheredonebyTypeC,RGBclipping.Thespectrumbarisshownbanded.

sR

sV

V

R



disp 15.4286

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m



disp 15.4286

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m

�3

0.380.420.460.500.540.580.620.660.70

λ µ/ m

No RGB clipping, no RGB gamma encodingLam L* a* b* R G B0.38 0.0 5.5 -9.2 0.3 -0.3 1.80.39 0.1 16.9 2- 5.0 0.9 -0.8 5.50.40 0.4 53.0 5- 1.1 3.0 -2.6 18.50.41 1.1 105.2 8- 5.6 9.1 -8.0 56.50.42 3.6 175.9 1- 34.2 27.4 2- 4.5 175.70.43 10.3 221.0 1- 71.4 53.9 4- 9.9 376.90.44 17.0 215.6 1- 77.2 56.7 5- 6.6 474.60.45 23.0 185.5 1- 68.0 37.6 4- 6.1 480.40.46 29.4 141.2 1- 52.3 4.6 2- 5.5 450.90.47 36.2 70.2 1- 21.5 3- 7.9 8.9 345.10.48 44.1 2- 6.5 7- 7.8 7- 8.8 51.5 213.20.49 52.7 1- 34.8 3- 2.1 1- 14.2 96.5 115.00.50 63.6 2- 54.0 11.3 1- 57.2 156.2 56.60.51 76.3 2- 90.7 53.9 2- 09.6 240.0 16.60.52 87.5 2- 43.4 95.3 2- 36.0 324.8 1- 4.90.53 94.4 1- 96.6 122.7 2- 06.5 371.9 3- 1.10.54 98.2 1- 55.4 143.9 1- 36.6 384.8 4- 0.00.55 99.8 1- 14.3 159.6 3- 2.9 368.9 4- 3.20.56 99.8 7- 1.6 166.5 100.8 329.1 4- 2.30.57 98.1 2- 7.4 166.2 256.4 267.1 3- 8.10.58 94.7 16.6 161.0 416.0 189.7 3- 1.80.59 89.7 57.3 153.1 551.3 108.5 2- 4.50.60 83.5 90.0 142.8 630.4 39.3 1- 7.50.61 76.3 111.3 131.0 631.4 -7.2 1- 1.80.62 68.1 120.1 117.1 556.8 2- 8.9 -7.60.63 58.5 117.6 100.8 427.0 3- 2.0 -4.70.64 48.9 109.4 84.3 301.6 2- 7.0 -2.70.65 39.1 96.7 67.4 192.4 1- 8.9 -1.50.66 29.7 82.0 51.1 112.4 1- 1.6 -0.80.67 20.8 66.9 35.9 59.7 -6.3 -0.40.68 13.8 54.7 23.8 32.0 -3.4 -0.20.69 7.4 43.1 12.8 15.5 -1.7 -0.10.70 3.7 29.5 6.4 7.8 -0.9 -0.1

With RGB clipping, no RGB gamma encodingLam L* a* b* R G B0.38 0.7 4.2 -8.2 0.3 0.0 1.80.39 2.1 12.9 2- 2.0 0.9 0.0 5.50.40 7.0 34.1 4- 0.1 3.0 0.0 18.50.41 17.3 49.7 5- 8.4 9.1 0.0 56.50.42 32.4 72.4 8- 5.6 27.4 0.0 175.70.43 40.8 83.1 9- 3.5 53.9 0.0 255.00.44 41.1 83.3 9- 2.9 56.7 0.0 255.00.45 38.5 81.8 9- 7.4 37.6 0.0 255.00.46 33.1 79.5 1- 06.4 4.6 0.0 255.00.47 37.3 64.0 9- 9.5 0.0 8.9 255.00.48 52.4 13.7 6- 4.0 0.0 51.5 213.20.49 61.9 3- 0.4 1- 7.2 0.0 96.5 115.00.50 73.2 6- 0.1 26.0 0.0 156.2 56.60.51 85.9 8- 1.4 67.1 0.0 240.0 16.60.52 87.7 8- 6.2 83.2 0.0 255.0 0.00.53 87.7 8- 6.2 83.2 0.0 255.0 0.00.54 87.7 8- 6.2 83.2 0.0 255.0 0.00.55 87.7 8- 6.2 83.2 0.0 255.0 0.00.56 91.6 5- 4.9 87.9 100.8 255.0 0.00.57 97.1 2- 1.6 94.5 255.0 255.0 0.00.58 89.1 -6.4 88.7 255.0 189.7 0.00.59 77.1 19.0 80.4 255.0 108.5 0.00.60 63.6 51.7 72.0 255.0 39.3 0.00.61 53.2 80.1 67.2 255.0 0.0 0.00.62 53.2 80.1 67.2 255.0 0.0 0.00.63 53.2 80.1 67.2 255.0 0.0 0.00.64 53.2 80.1 67.2 255.0 0.0 0.00.65 47.0 72.9 61.2 192.4 0.0 0.00.66 36.7 60.9 51.1 112.4 0.0 0.00.67 26.7 49.4 39.5 59.7 0.0 0.00.68 18.7 40.1 28.7 32.0 0.0 0.00.69 11.2 31.5 17.7 15.5 0.0 0.00.70 5.9 24.1 9.3 7.8 0.0 0.0

9. Single ray / Illuminant Equal Energy / Compression Type C / RGB clippingIlluminantEqualEnergyhasaflatspectrum.CompressionisdonebyTypeC,RGBclipping.Thespectrumbarsareshownbandedandcontinuous.ThetableshowslinearRGBvalues,thebarswerecalculatedwithgammaencodingforsRGB.RGBclippingdoesnotcreatebalanceddistributionsofcolors.

�4

10. Single ray / Illuminant Equal Energy / Compr. Type A / CIELab

0.380.420.460.500.540.580.620.660.70

λ µ/ m

No gamut compression, no RGB gamma encodingLam L* a* b* R G B0.38 0.0 5.5 -9.2 0.3 -0.3 1.80.39 0.1 16.9 2- 5.0 0.9 -0.8 5.50.40 0.4 53.0 5- 1.1 3.0 -2.6 18.50.41 1.1 105.2 8- 5.6 9.1 -8.0 56.50.42 3.6 175.9 1- 34.2 27.4 2- 4.5 175.70.43 10.3 221.0 1- 71.4 53.9 4- 9.9 376.90.44 17.0 215.6 1- 77.2 56.7 5- 6.6 474.60.45 23.0 185.5 1- 68.0 37.6 4- 6.1 480.40.46 29.4 141.2 1- 52.3 4.6 2- 5.5 450.90.47 36.2 70.2 1- 21.5 3- 7.9 8.9 345.10.48 44.1 2- 6.5 7- 7.8 7- 8.8 51.5 213.20.49 52.7 1- 34.8 3- 2.1 1- 14.2 96.5 115.00.50 63.6 2- 54.0 11.3 1- 57.2 156.2 56.60.51 76.3 2- 90.7 53.9 2- 09.6 240.0 16.60.52 87.5 2- 43.4 95.3 2- 36.0 324.8 1- 4.90.53 94.4 1- 96.6 122.7 2- 06.5 371.9 3- 1.10.54 98.2 1- 55.4 143.9 1- 36.6 384.8 4- 0.00.55 99.8 1- 14.3 159.6 3- 2.9 368.9 4- 3.20.56 99.8 7- 1.6 166.5 100.8 329.1 4- 2.30.57 98.1 2- 7.4 166.2 256.4 267.1 3- 8.10.58 94.7 16.6 161.0 416.0 189.7 3- 1.80.59 89.7 57.3 153.1 551.3 108.5 2- 4.50.60 83.5 90.0 142.8 630.4 39.3 1- 7.50.61 76.3 111.3 131.0 631.4 -7.2 1- 1.80.62 68.1 120.1 117.1 556.8 2- 8.9 -7.60.63 58.5 117.6 100.8 427.0 3- 2.0 -4.70.64 48.9 109.4 84.3 301.6 2- 7.0 -2.70.65 39.1 96.7 67.4 192.4 1- 8.9 -1.50.66 29.7 82.0 51.1 112.4 1- 1.6 -0.80.67 20.8 66.9 35.9 59.7 -6.3 -0.40.68 13.8 54.7 23.8 32.0 -3.4 -0.20.69 7.4 43.1 12.8 15.5 -1.7 -0.10.70 3.7 29.5 6.4 7.8 -0.9 -0.1

With gamut compression, no RGB gamma encodingLam L* a* b* R G B0.38 0.0 0.2 -0.3 0.0 0.0 0.10.39 0.1 0.7 -1.0 0.1 0.0 0.20.40 0.4 2.0 -1.9 0.3 0.0 0.50.41 1.1 5.8 -4.7 1.1 0.0 1.20.42 3.6 18.9 1- 4.5 3.4 0.0 4.00.43 10.3 34.9 2- 7.1 9.3 0.0 13.60.44 17.0 44.4 3- 6.5 17.7 0.0 29.30.45 23.0 53.6 4- 8.5 26.7 0.0 56.10.46 29.4 65.6 7- 0.8 31.3 0.0 120.30.47 36.2 49.8 8- 6.3 0.0 12.5 198.20.48 44.1 1- 0.4 3- 0.7 0.1 41.1 83.30.49 51.9 3- 1.5 -7.5 0.0 65.3 62.50.50 59.5 4- 1.0 1.8 0.0 91.7 65.80.51 68.4 4- 9.5 9.2 0.1 129.5 76.20.52 76.2 6- 0.7 23.8 0.2 172.3 68.80.53 81.1 7- 1.9 44.9 0.0 204.8 41.50.54 83.7 8- 2.3 76.1 0.0 226.4 3.70.55 84.9 5- 8.9 82.2 62.6 215.8 0.00.56 84.9 3- 5.6 82.9 128.8 196.1 0.30.57 83.7 1- 3.8 83.6 191.4 169.3 0.00.58 81.3 8.5 82.8 250.6 136.0 0.30.59 77.8 20.9 56.0 255.0 110.1 24.20.60 73.4 31.0 49.2 254.5 85.1 26.40.61 68.4 42.2 49.7 254.3 59.7 19.40.62 62.7 55.6 54.3 254.9 34.4 10.20.63 56.0 72.7 62.3 254.9 9.1 2.30.64 49.2 75.8 58.4 213.4 0.0 1.50.65 39.1 63.8 44.4 127.5 0.0 2.10.66 29.7 53.4 33.3 72.9 0.0 2.00.67 20.8 43.0 23.1 37.9 0.0 1.60.68 13.8 34.7 15.1 19.9 0.0 1.20.69 7.4 27.3 8.1 9.6 0.0 0.70.70 3.7 17.2 3.7 4.8 0.0 0.4

Thesamemethodasinthepreviouschapter,butnowthecompressionisdonebyTypeAinCIELab.Thespectrumbarslookbetterbalanced.ThetableshowslinearRGBvalues,thebarswerecalculatedwithgammaencodingforsRGB.ThespectrumbarslookbetterbalancedbecauseofCIELabgamutcompression.

�5

0.380.420.460.500.540.580.620.660.70

λ µ/ m

No gamut compression, no RGB gamma encodingLam X•100 Y•100 Z•100 R G B0.38 0.1 0.0 0.6 0.3 -0.3 1.80.39 0.4 0.0 2.0 0.9 -0.8 5.50.40 1.4 0.0 6.8 3.0 -2.6 18.50.41 4.4 0.1 20.7 9.1 -8.0 56.50.42 13.4 0.4 64.6 27.4 2- 4.5 175.70.43 28.4 1.2 138.6 53.9 4- 9.9 376.90.44 34.8 2.3 174.7 56.7 5- 6.6 474.60.45 33.6 3.8 177.2 37.6 4- 6.1 480.40.46 29.1 6.0 166.9 4.6 2- 5.5 450.90.47 19.5 9.1 128.8 3- 7.9 8.9 345.10.48 9.6 13.9 81.3 7- 8.8 51.5 213.20.49 3.2 20.8 46.5 1- 14.2 96.5 115.00.50 0.5 32.3 27.2 1- 57.2 156.2 56.60.51 0.9 50.3 15.8 2- 09.6 240.0 16.60.52 6.3 71.0 7.8 2- 36.0 324.8 1- 4.90.53 16.5 86.2 4.2 2- 06.5 371.9 3- 1.10.54 29.0 95.4 2.0 1- 36.6 384.8 4- 0.00.55 43.3 99.5 0.9 3- 2.9 368.9 4- 3.20.56 59.4 99.5 0.4 100.8 329.1 4- 2.30.57 76.2 95.2 0.2 256.4 267.1 3- 8.10.58 91.6 87.0 0.2 416.0 189.7 3- 1.80.59 102.6 75.7 0.1 551.3 108.5 2- 4.50.60 106.2 63.1 0.1 630.4 39.3 1- 7.50.61 100.3 50.3 0.0 631.4 -7.2 1- 1.80.62 85.4 38.1 0.0 556.8 2- 8.9 -7.60.63 64.2 26.5 0.0 427.0 3- 2.0 -4.70.64 44.8 17.5 0.0 301.6 2- 7.0 -2.70.65 28.3 10.7 0.0 192.4 1- 8.9 -1.50.66 16.5 6.1 0.0 112.4 1- 1.6 -0.80.67 8.7 3.2 -0.0 59.7 -6.3 -0.40.68 4.7 1.7 0.0 32.0 -3.4 -0.20.69 2.3 0.8 -0.0 15.5 -1.7 -0.10.70 1.1 0.4 -0.0 7.8 -0.9 -0.1

With gamut compression, no RGB gamma encodingLam X•100 Y•100 Z•100 R G B0.38 0.0 0.0 0.0 0.0 0.0 0.10.39 0.0 0.0 0.1 0.1 0.0 0.20.40 0.1 0.0 0.2 0.3 0.0 0.50.41 0.3 0.1 0.5 1.1 0.0 1.20.42 0.8 0.4 1.5 3.4 0.0 4.00.43 2.5 1.2 5.2 9.3 0.0 13.60.44 4.9 2.3 11.1 17.7 0.0 29.30.45 8.3 3.8 21.1 26.7 0.0 56.10.46 13.6 6.0 45.1 31.3 0.0 120.30.47 15.8 9.1 74.5 0.0 12.5 198.20.48 11.7 13.9 33.0 0.1 41.1 83.30.49 13.6 20.1 26.3 0.0 65.3 62.50.50 17.5 27.6 28.8 0.0 91.7 65.80.51 23.6 38.5 34.5 0.1 129.5 76.20.52 29.1 50.3 33.7 0.2 172.3 68.80.53 31.7 58.6 25.0 0.0 204.8 41.50.54 32.0 63.6 12.0 0.0 226.4 3.70.55 40.4 65.7 10.6 62.6 215.8 0.00.56 48.3 65.7 10.3 128.8 196.1 0.30.57 54.7 63.5 9.4 191.4 169.3 0.00.58 59.6 59.0 8.4 250.6 136.0 0.30.59 58.4 52.8 16.1 255.0 110.1 24.20.60 55.0 45.8 15.7 254.5 85.1 26.40.61 50.9 38.5 12.0 254.3 59.7 19.40.62 46.8 31.2 7.3 254.9 34.4 10.20.63 42.7 23.9 3.2 254.9 9.1 2.30.64 34.6 17.8 2.2 213.4 0.0 1.50.65 20.8 10.7 1.8 127.5 0.0 2.10.66 11.9 6.1 1.3 72.9 0.0 2.00.67 6.3 3.2 0.9 37.9 0.0 1.60.68 3.3 1.7 0.6 19.9 0.0 1.20.69 1.6 0.8 0.3 9.6 0.0 0.70.70 0.8 0.4 0.2 4.8 0.0 0.4

11. Single Ray / Linear Spectrum / Illuminant Equal Energy / Compr. Type A / CIELabThisisnottheprismexperiment.Thewavelengthisnowlinearlydistributedalongthehorizontalaxis.Graphicslikethisappearoftenintextbooks,mostlywrongthough.Modernspectrophoto-metersusegratingsinsteadofprisms.Thenthebarwouldlooklikehere.ThetableshowslinearRGBvalues.InsteadofLabvalues(thesameasonthepreviouspage)theCIEXYZvaluesareshown.ThebarswerecalculatedwithgammaencodingforsRGB.

�6

12. Multiple ray / Illuminant Equal Energy / Compr. Type B / CIELab

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m

Illuminant Equal Energy

Acontinuouslightbandwithflatspectrumissimulatedbymultiplerays.Eachofthemisinter-pretedaccordingtochapter8.Thecontentoftheinterpolatedmeasurementarrayismultipliedbythecolor-matchingfunctionsandtheslopefunction.ThensummedupinasecondarraywhichcontainsCIEXYZvaluesforeachwavelength.ThecontentoftheXYZarrayisnorma-lizedforYmax=�afterfinishingthemeasurement.Thesumapproximatesanintegration.

In themiddlewehavewhite light.At theendswecanseecolor fringes.This isGoethe’simportantobservationonwhichhebasedhisattackagainstNewton:colorsappearat theboundariesoflightandshadow.

�7

13. Multiple ray / Illuminants A, D50, D65,D75 / Compr. Type B / CIELab

Differentilluminantsgeneratedifferentshadesofwhiteinthemiddle.IlluminantAisaPlanck-ianradiatorwithcolortemperature2856K,asproducedbyadomestictungstenbulb.Candlelightwouldlookeven‘warmer’,whichmeansithasalowercolortemperature,about�900K.Graphicsfortypicalspectraarefoundinbooks[�0]andindocumentsbytheauthor[�9].Thevaluesinthemeasurementarrayaremultipliedbyoneofthesespectraaswell,inaddi-tiontothemultiplicationbycolor-matchingfunctionsandslopefunctions.Inreallifethediscrepanciesfordifferentilluminantswouldbelessobviousbecauseofadap-tation:thetungstenorcandleyellowwouldlooklessyellow-ishandnorthskylightD75wouldlooklessblue-ish.Thesimulationofperceivedcolorsishandledincolortheorybychromaticadaptationtrans-forms[�0],[�4],[2�].Thesearenotappliedhere.

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m

Illuminant A

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m

Illuminant D65

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m

Illuminant D50

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m

Illuminant D75

�8

14. Goethe’s explanations

ThegraphicshowsGoethe’sFünfte Tafel. Hereitisanewdrawingbytheauthor,basedonaprintin[2],asaccurateaspossible.Thesmallimagetopleftvisualizesthreesituationsforalightband,representedbytworays:withoutrefraction,refractedbyaparallelplateandrefractedbytheupperprism.Colorfringesareemphasized.Thelargeimageshouldmaketherefractioneffectbyoneprismmuchclearer.Theraygeometryintheprism(A)iswrong,butthisismoreasymbolicaldrawingwhichshows’lightversusshadow’.

Thecross-section(B)isapproximatelythesameasinthepreviouschapters.ButthensaidGoethe:’thecross-section,wheretheellipseisdrawn,isabouttheonewhereNewtonandhisfollowersperceive,fixandmeasuretheimage’.

DoesitmeanthatGoetheexpectedaspectrumwithoutwhiteinthemiddle,likeinthecross-sections(C)to(E)?Justanoverlayofedgeeffects?Itseemsso,butthenhewereterriblywrong-theraysinthemiddlecannotbeignored.Goetheusedalightband,Newtonusedforhiscrucial experimentsathinray.Andheknewalreadythatlightbandsdeliverwhiteinthemiddle.

A

B

C

D

E

16

�9

15. Conclusions

TheConclusionsrefertotheIntroduction,chapter�.Furtheronsomeremarksontheperceivedbrightnessofblueareadded.

A [2,Zweiter Teil, Konfession des Verfassers ]Aberwieverwundertwarich,...’

Aprismrefractsalightbandoradensebundleof(fictitious)rayswithoutstrongcoloreffectsinthemiddlebecausetheserayssumuptowhitelight.Goethewasnotawareofthissuper-position.Thereforeheemphasizedcoloreffectscorrectlyattheboundaryofthebundle.New-ton’scrucial experimentswereessentiallydonewiththinrays.ItisnotunderstandablewhyGoethedidnotdiscussthecaseforathinray.Itseemsthatheregardedthisasaquiteunnaturaltestconditionwhichhadnothingtodowithreallife.InfacthedidnotreadOpticks carefullyoratall.Forexample,theellipse(C)inhisdrawingwasclearlydescribedbyNewtonas‘oblong’,theenvelopofasequenceofcircles.

B[2,Zweiter Teil, Polemischer Teil ]’Also,umbeimRefraktionsfallezuverweilen,...’

Goetheassumesthatrefractionitselfdoesnotcreatecoloreffects.Thiswouldrequireanimagewhichisrefractedandshiftedaswell,andwhichhasboundaries,becauseitisanimage.Butifitisrefractedthenitisshifted-theargumentisnotunderstandable.Ontheotherhandheisrightinacertainsense,thoughwithoutbeingawareof:refractionitselfdoesnotcolorizeanything.Thecolorordispersionisaresultofdifferentrefractionindicesfordifferentwavelengths,fordifferentspectralcolors.

C[2,Zweiter Teil, Beiträge zur Optik ]’UnterdeneigentlichenfarbigenErscheinungensindnurzwei,...’

Goethe’sErste Tafel showscolorwheels.ItseemsthathehadacceptedNewton’smodeltoacertainextent.

Goethe’smodeluses(alsoaccordingto[7])threeprimariesyellow,blue,redandthreesecon-dariesorange,violet,green.Ontheotherhandheconsidersonlyyellowandblueaspurecolors.Maybethiswasjustanunnecessarycomplication.

Goetheknewalmostalltheothercontributorstocolorscience,asmentionedinthesamebook[7],butnotyetPhilipp Otto Runge,whopublished�8�0thefirstthreedimensionalcolorspace,asphere.

The Blue Mystery

Insimulationsweperceiveinthespectrumbarsthesmallpartforpureblueonmonitorsastoobright.ThecolorreproductionisbasedonthesRGBmodelwhichdescribeswithsufficientaccuracycommoncathoderaytubemonitors(realmonitorsarecalibratedbyinstruments,aprocesswhichintroducestheactualparametersintothecolormanagementsystem).

Thecontributionofbluetotheluminanceisgivenbyequationslikethis:

L=0.3R+0.6G+0.�B

Withaccuratenumbersthisiscolorimetricallycorrect.Isbluereallysixorseventimesdarkerthangreen?Theauthorcouldnotprovesucharatiobyflickertests.AnexplanationmightbetheHelmholtz-Kohlrausch effect[�3]whichmeans:fullysaturatedcolorsappearbrighterthanlesssaturatedcolors.Thetableinchapter�0showsthehighestsaturationsforredat0.63µm,forgreenat0.54µmandforblueat0.47µm.

20

16. Hoffmann’s prism experiment

Aslideprojectorisusedaslightsource.Theslideisametalplatewithathinhorizontalslit.Thecylinderwiththeprismcanberotated.Thespectrumbarappearsonanadjustableglassplatewhichisgroundononeside.Themechanicalsystemcanbefoldedandstoredtogetherwiththeprojectorinasuitcase.Astudent’sprojectbyMr.BurhanPrimanintyo..

Bestviewzoom200%at72dpi.

2�

17. Reverse problem and inverse appearance

InSeptember20�2theauthorreceivedamessagebyDr.StephenR.J.Williams,aUK-basedGeoscientist:

EyeR�

R2

v�

v2

r2

r�

Theimagesinyourchapter�2seemtoexplainhowthefringesareproduced.Myinter-pretation(seeattachedillustration)ofyourdiagramindicatesthatobserverwillseebluefringesattopofapertureimageandred/yellowfringesatbottomofapertureimage.ButwhenIlookthrougharealprismIseebluefringesatthebottomoftheapertureimageandred/yellowfringesatthetop.Thisisoppositetothatinthediagram.

Dr.Williamsisright.Laterheprovidedthelink[26],whichisofhighvalue.Butthisreportdoesnotexplaintheprobleminaconvincingmanner,doesnotexplainwhatiscalledbelowtheinverse appearance phenomenon.NotevenGoethehimselfhaddescribedthediscrepancybetweenhisdrawingFünfte Tafelinchapter�4andhisviewthroughtheprism.ThedrawingreproducesmoreorlessNewton‘sapproach(withsomeerrorsthough,concerningtheanglesofrefraction).Itshowsthecolorbandsonascreen,similartoalltheotherillustrationshereinthisdocument.Lookingthroughaprismisin[26]calledthereverse problem-exactlyGoethe‘sapproach,butnotinhisdrawing.Theinversion,asobservedbyDr.Williams,isherecalledinverse ap-pearance phenomenon.

TheexplanationfollowsDr.Williams‘ideawithminormodifications.Attheleftwehaveablackcardboardwithawhiterectangle,maybelikeoneofthosewhichGoethehadused[27].Oneeyeoftheobserverisshownattheright.WeareinterpretingtworaysR�andR2.RayR�couldbegeneratedbyavioletrayv�,aredrayr�oranyotherraybetween(inmodernnomen-clature:orange,yellow,green,cyan,blue).Nowweseethatblue,cyanandgreenactuallycannotbegenerated,becausethecardboardisblackatthesepositions.Thereforeonlyredandyellowcontributionsremainandthatisthecolorofthefringe.ForrayR2thesituationissimilar,butviolet,blueandcyanremain.Dr.Williamsemphasizesthatgreenhardlyappearsatedges,opposedtofullydevelopedrainbowspectrafornarrowaperturesorrectangles.ThiscanbeconfirmedbyexperimentsusingtheGoethe Kit[27].Somewhatsimplified:thetopfringeisred/yellow,thebottomfringeblue/cyan.Thisisindeedaninverseappearance,comparedtotheprojectionofraysthroughaprismontoascreen,assimulatedinchapter�2.

22

18.1 The colors of darkness

InJuly20�5theauthorfoundinanewspaperaninterestingarticlebyMichaelJäger[28]aboutanewbookbyOlafMüller,concerningGoethe’sinvestigations[29].ThereisanassociatedwebsitebyOlafMüller[30].

M.Jägersays:„InderMitteseinesSpektrumssiehtGoethedieFarbePurpur,diebeiNewtonnichtvorkommt.BeiGoethekommtdieFarbeGrünnichtvor.Müllerkannnachweisen,daßbisjetztalleVersu-che,dasErgebnisdesgoetheschenExperiments“orthodox”,alsonewtonischwegzuerklären,gescheitertsind.GewisskannmandasPurpuralskomplizierteÜberlagerungderFarbendesnewtonschenSpektrumsinterpretieren…“

Thisinterpretationisfairlysimple:ablackgap(darkness)inthegeneratingobjectlightbandismappedbehindtheprismontothescreennotasblackbutasapseudospectrumwhichcontainsindeedpurpleasamixtureofredandblue.(cont.nextpage)

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m


23

18.2 The colors of darkness

ThistestillustratesJäger’sDunkelstrahlen[28],whichreferperhapstoGoethe’sremarkinhisConfession des Verfassers[2],[32]:„EineschwarzeScheibeaufhellemGrundmachtaberaucheinfarbigesundgewissermaßennochprächtigeresGespenst.WennsichdortdasLichtinsovielerleiFarbenauflös’t,sagteichzumirselbst:somüßtejahierauchdieFinsternißalsinFarbenaufgelös’tangesehenwerden.“

Thisvisualizationishighlyartificial.Ifthegeometryandotherparametersaremodified,thentheresultwillbedifferent,seebelow.This‘verification’ofGoethe’stheoryiswidelyafake.

Referringto[30],Müller’swebsite:Thedarknessdoesnotcreatetheprimariescyan,magentaandyellowforthesubtractivecolormixture.It’sjustanoverlayofspectrumparts,ofcoursegeneratedbylightandnotbydarkness,somewhatoptimizedfortheresultpurple=magenta.Cyanandyellowbelonganywaytothespectralcolors,butthecolorpurpledoesn’t.

AcriticalinterpretationofOlafMüller’sbookcanbefoundin[3�].

0 10000.380.420.460.500.540.580.620.660.70

λ µ/ m


24

19. A natural rainbow

Thisimageshowsanaturalrainbow.Thesaturationinthewindowwasslightlyenlargedinordertoshowtwoeffects:

�)Therainbowcolorscontainthecolorcyanbetweengreenandblue,whichismissinginNewton‘sdescriptions.

2)Beyondblueonecanseepurpleorviolet.Theexistenceofthiscolorattheblueendofthespectrum(notattheredend)canbeconsideredasagoodreasonforarrangingthelinearspectrumofvisiblecolorsonacircle.Infactwehavetwometamericpurples:oneattheblueendofthespectrum,thereforeaspectralcolor,andtheotherbymixingblueandred.

PhotobycourtesyofNorbertKustosCroppedandmodifiedwithpermission

25

20.1 References

[�] IsaacNewton Opticks GreatMindSeries,Prometheus,2003

[2] JohannWolfgangGoethe GeschichtederFarbenlehre ErsterTeil,zweiterTeil,dtvGesamtausgabe4�,42 DeutscherTaschenbuchverlag,München,�963 ThankstoVolkerHoffmannforpreservingandprovidingthebook

[3] W.Heisenberg DieGoethe’scheunddieNewton’scheFarbenlehreimLichtedermodernenPhysik WandlungenindenGrundlagenderNaturwissenschaft.4.Auflage,VerlagS.Hirzel,Leipzig,�943

[4] Chr.Gerthsen Physik SpringerVerlag,Berlin...,�966

[5] N.Guicciardini Newton:EinNaturphilosophunddasSystemderWelten SpektrumderWisssenschaftVerlagsgesellschaft,Heidelberg,�999

[6] R.Breuer(Chefredakteur) Farben SpektrumderWisssenschaftVerlagsgesellschaft,Heidelberg,2000

[7] N.Silvestrini+E.P.Fischer IdeeFarbe,FarbsystemeinKunstundWissenschaft Baumann&StromerVerlag,Zürich,�994

[8] K.Kahnmeyer+H.Schulze Realienbuch Velhagen&Klasing,BielefeldundLeipzig,�9�2

[9] J.D.Foley+A.van Dam+St.K.Feiner+J.F.Hughes ComputerGraphics Addison-Wesley,ReadingMassachusetts,...,�993

[�0] R.W.G.Hunt MeasuringColour FountainPress,England,�998

[��] R.W.G.Hunt TheReproductionofColour,sixthedition JohnWiley&Sons,Chichester,England,2004

[�2] E.J.Giorgianni+Th.E.Madden DigitalColorManagement Addison-Wesley,ReadingMassachusetts,...,�998

[�3] G.Wyszecki+W.S. Stiles ColorScience JohnWiley&Sons,NewYork,...,�982

[�4] Ph.Green+L.MacDonald(Ed.) ColourEngineering JohnWiley&Sons,Chichester,England,2002

26

[�5] SchottAG OptischerGlaskatalog-DatentabelleEXCEL28.04.2005 http://www.schott.com

[�6] Wikipedia SellmeierEquation http://en.wikipedia.org/wiki/Sellmeier_equation

[�7] M.Stokes+M.Anderson+S.Chandrasekar+R.Motta AStandardDefaultColorSpacefortheInternet-sRGB,�996 http://www.w3.org/graphics/color/srgb.html[�9] G.Hoffmann Documents,mainlyaboutcomputervision http://docs-hoffmann.de/howww4�a.html

[20] G.Hoffmann HardwareMonitorCalibration http://docs-hoffmann.de/caltutor270900.pdf

[2�] G.Hoffmann CIELabColorSpace http://docs-hoffmann.de/cielab03022003.pdf

[22] G.Hoffmann CIE(�93�)ColorSpace http://docs-hoffmann.de/ciexyz29082000.pdf

[23] G.Hoffmann GamutforCIEPrimarieswithVaryingLuminance http://docs-hoffmann.de/ciegamut�60�2003.pdf

[24] G.Hoffmann ColorOrderSystemsRGB/HLS/HSB http://docs-hoffmann.de/hlscone0305200�.pdf

[25] EarlF.Glynn Collectionoflinks,everythingaboutcolorandcomputers http://www.efg2.com

[26] ZurFarbenlehre(inEnglish,authorunknown) http://www.mathpages.com/home/kmath608/kmath608.htm

[27] GoethesExperimentezuLichtundFarbe Experimentalkitwithprism,Goethe‘scolorcards,posters,textbookandfacsimileprint ofGoethe‘sBeyträge zur Optik (�79�) KlassikStiftungWeimar2007 VerlagBien&GierschProjektagentur

[28] MichaelJäger:Darkness,alterFreund derFreitag/Nr.28/9.Juli20�5/Seite�5

[29] http://www.fischerverlage.de/buch/mehr_licht/9783�00022073 OlafMüller:MehrLicht.GoethemitNewtonimStreitumdieFarben S.FischerVerlag,20�5

[30] http://farbenstreit.de/buchpremiere-mehr-licht/

20.2 References

http://www.schott.com

http://en.wikipedia.org/wiki/Sellmeier_equation

http://www.w3.org/graphics/color/srgb.html

http://docs-hoffmann.de/howww41a.html

http://docs-hoffmann.de/caltutor270900.pdf

http://docs-hoffmann.de/cielab03022003.pdf

http://docs-hoffmann.de/ciexyz29082000.pdf

http://docs-hoffmann.de/ciegamut16012003.pdf

http://docs-hoffmann.de/hlscone03052001.pdf

http://www.efg2.com

http://www.mathpages.com/home/kmath608/kmath608.htm

http://www.fischerverlage.de/buch/mehr_licht/9783100022073

http://farbenstreit.de/buchpremiere-mehr-licht/

27

[3�] http://www.spektrum.de/rezension/buchkritik-zu-mehr-licht/�347549

[32] ZurFarbenlehre,vonGoethe ErsterBand,Tübingen,�8�0 Faksimile-DruckvonGoethesFarbenlehre (nur)Band�undConfession des Verfassers DiebibliophilenTaschenbücher HarenbergKommunikation,Dortmund,�979

Thisdocument: http://docs-hoffmann.de/prism�6072005.pdf

20.3 References

GernotHoffmannSeptember�5/2005–May05/20�9

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http://www.spektrum.de/rezension/buchkritik-zu-mehr-licht/1347549

http://docs-hoffmann.de/prism16072005.pdf

http://docs-hoffmann.de/