gernot hoffmann newton’s prism experiment and goethe’s
TRANSCRIPT
�
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
ThisdocumentcanbereadbyAdobeAcrobat.Somesettingsareessential:thecolorspacesRGBfortheappearance;theresolution72dpiforpixelsynchronizedimages.Bestviewzoom200%(titleimageandphotoonp.20).
SettingsforAcrobat
Edit/Preferences/General/PageDisplay(sinceversion6)CustomResolution72dpi
Edit/Preferences/General/ColorManagement(fullversiononly)sRGB
EuroscaleCoatedorISOCoatedorSWOPGrayGamma2.2
Areasonable reproductionof thecolors ispossibleonlybyacalibratedcathode ray tubemonitororahighendLCDmonitor(nohopefornotebooksorlaptops).Themonitorshouldbecalibratedoradjustedbythesetestpatterns:
CalTutor
http://docs-hoffmann.de/caltutor270900.pdf
Thisdocumentisprotectedbycopyright.Anyreproductionrequiresapermissionbytheauthor.Thisshouldbeconsideredasaprotectionagainstbadorwrongcopying.TheauthorprovidesondemandfilesinRGBforthespecificpurposeinoriginalqualityandfilesforCMYKoffsetprinting(whichcannotreproducesRGBcolorscorrectly),adjustedasgoodaspossible.
Copyright
GernotHoffmann
August2005andlater
Printingthisdocaccuratelyrequiresacalibratedprinter,preferablyaninkjetorhighendcolorlaserprinter.Officeprinterscannotreproducethespectrumbarsreasonably.
Accurateprintingrequiresacalibratedprinter
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
Glass BK7LBlue 0.3800LRed 0.7000nBlue 1.5337nRed 1.5131
rho1 52.0000rho2 0.0000
For bluealf1 82.0000bet1 40.2147alf2 31.2764bet2 19.7853defl 53.2764
disp 1.5672
Glass SF15LBlue 0.3800LRed 0.7000nBlue 1.7548nRed 1.6890
rho1 31.4000rho2 31.0000
For bluealf1 61.4000bet1 30.0221alf2 61.2600bet2 29.9779defl 62.6600
disp 7.1119
Glass SF15LBlue 0.3800LRed 0.7000nBlue 1.7548nRed 1.6890
rho1 55.0000rho2 19.0000
For bluealf1 85.0000bet1 34.5899alf2 48.8484bet2 25.4101defl 73.8484
disp 5.7646
Glass SF15LBlue 0.3800LRed 0.7000nBlue 1.7548nRed 1.6890
rho1 19.0000rho2 55.0000
For bluealf1 49.0000bet1 25.4729alf2 84.0482bet2 34.5271defl 73.0482
disp 15.4286
4. Geometry for maximal dispersion
Forapracticalprismexperimentthedispersionshouldbeaslargeaspossible.Flintglassisthebetterchoice.Theoptimalanglescanbefoundbytrialanderror.Thesimulationbelowconfirmsthetestresults.Leftcrownglass,rightflintglass.Theuppertwoimagesshowthesymmetricalcase.Thelowershowtheoptimalcase.Theoutputangleβ2shouldbenearto90°fortheshortestwavelength(violet).Inthemiddleimagesonecanseethatlargeinputanglesα�donotdeliverthebestresults.
Crownglass Flintglass
Glass BK7LBlue 0.3800LRed 0.7000nBlue 1.5337nRed 1.5131
rho1 1.0000rho2 55.0000
For bluealf1 31.0000bet1 19.6215alf2 83.5210bet2 40.3785defl 54.5210
disp 6.4668
9
5. Ray visualization and a photo
Glass SF15LBlue 0.3800LRed 0.7000nBlue 1.7548nRed 1.6890
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
Glass SF15LBlue 0.3800LRed 0.7000nBlue 1.7548nRed 1.6890
rho1 19.0000rho2 54.0000For bluealf1 49.0000bet1 25.4729alf2 84.0482bet2 34.5271defl 73.0482
disp 15.4286
0 10000.380.420.460.500.540.580.620.660.70
λ µ/ m
Glass SF15LBlue 0.3800LRed 0.7000nBlue 1.7548nRed 1.6890
rho1 19.0000rho2 54.0000For bluealf1 49.0000bet1 25.4729alf2 84.0482bet2 34.5271defl 73.0482
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
Illuminant Equal Energy
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
Illuminant Equal Energy
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
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
WebsiteLoadbrowser/Clickhere