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March 17, 2016 CH 35 Interference
I.
OpticalInterference:
A. Interferenceoflightwaves,appliedinmanybranchesofscience.
B. TheblueofthetopsurfaceofaMorphobutterflywingisdueto
opticalinterferenceandshiftsincolorasyourviewingperspective
changes.(PhilippeColombi/PhotoDisc//GettyImages)
II.
LightasaWave:
A. Huygen’sPrinciple:
1.
Allpointsonawavefrontserveaspointsourcesofsphericalsecondary
wavelets.Afteratimet,thenewpositionofthewavefrontwillbethatofa
surfacetangenttothesesecondarywavelets.
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March 17, 2016 B. LightasaWave,LawofRefraction:
1.
Thelawofrefractionstillapplies:
2.
Proof:
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March 17, 2016 C. LightasaWave,WavelengthandLawofRefraction:
1.
Thephasedifferencebetweentwolightwavescanchangeifthewaves
travelthroughdifferentmaterialshavingdifferentindexesofrefraction.
2.
Tofindtheirnewphasedifferenceintermsofwavelengths,wefirst
countthenumberN ofwavelengthsthereareinthelengthLofmedium1.
1
3.
Similarly,formedium2,
4.
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March 17, 2016 D. LightasaWave,RainbowsandOpticalInterference
1.
Lightwavespassintoawaterdropalongtheentiresidethatfacesthe
Sun.Differentpartsofanincomingwavewilltraveldifferentpathswithinthe
drop.
2.
Thatmeanswaveswillemergefromthedropwithdifferentphases.
Thus,wecanseethatatsomeanglestheemerginglightwillbeinphaseand
giveconstructiveinterference.
3.
Therainbowistheresultofsuchconstructiveinterference.
E. SampleProblems:
1.
Inthefigurebelow,assumethatthetwolightwaves,of
wavelength620nminair,areinitiallyoutofphasebyπrad.The
indexesofrefractionofthemediaaren1=1.45andn2=1.65.Whatarethe(a)
smallestand(b)secondsmallestvalueofLthatwillputthewavesexactlyin
phaseoncetheypassthroughthetwomedia?
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March 17, 2016 2.
Alaserbeamwithawavelengthandfrequencyinairof540nmand
5.6x1014Hzentersafluidwithrefractiveindex1.3atanangleof40ºwith
respecttothenormaltothesurface.Thefrequencyandwavelengthofthe
lightinthefluidareclosestto
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March 17, 2016 III.
Diffraction:
A. Ifawaveencountersabarrierthathasanopeningofdimensions
similartothewavelength,thepartofthewavethatpassesthroughthe
openingwillflare(spread)out—willdiffract—intotheregionbeyond
thebarrier.Theflaringisconsistentwiththespreadingofwavelets
accordingtoHuygensprinciple.Diffractionoccursforwavesofall
types.
B. Awavepassingthroughaslitflares(diffracts).
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March 17, 2016 C. Young’sInterferenceExperiment:
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March 17, 2016 1.
Thephasedifferencebetweentwowavescanchangeifthewavestravel
pathsofdifferentlengths.
2.
WhatappearsateachpointontheviewingscreeninaYoung’sdouble‐
slitinterferenceexperimentisdeterminedbythelengthdifferenceLofthe
raysreachingthatpoint.
3.
Forabrightfringe,Lmustbeeitherzerooranintegernumberof
wavelengths.Therefore,
4.
Foradarkfringe,Lmustbeanoddmultipleofhalfawavelength.
Therefore,
5.
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March 17, 2016 D. SampleProblems:
1.
SupposethatYoung'sexperimentisperformedwithblue‐greenlightof
wavelength500nm.Theslitsare1.20mmapart,andtheviewingscreenis
5.40mfromtheslits.Howfarapartarethebrightfringesnearthecenterof
theinterferencepattern?
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March 17, 2016 2.
AYoung’sinterferenceexperimentisperformedwith
monochromaticlightofwavelength632.8nm.Intheinterferencepattern
onascreen3.0mawayfromtheslits,thesecondminimumis5mmaway
fromthecenterofthepattern.Theseparationbetweentheslitsisclosest
to
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March 17, 2016 3.
Monochromaticlightofwavelength537nmstrikesascreencontaining
2slitsthatare5.0μmapartand2.0mfromaviewingscreen.Whatisthe
distanceonthescreenfromthecenteroftheinterferencepatterntothe
secondordermaximum?
4.
Adouble‐slitarrangementproducesinterferencefringesforsodium
light(λ=589nm)thatare0.20°apart.Whatistheangularfringeseparationif
theentirearrangementisimmersedinwater(n=1.33)?
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March 17, 2016 E. Coherence:
1.
FortheinterferencepatterntoappearonviewingscreenCinthe
figure,thelightwavesreachinganypointPonthescreenmusthaveaphase
differencethatdoesnotvaryintime.Whenthephasedifferenceremains
constant,thelightfromslitsS andS issaidtobecompletelycoherent.
1
2
2.
Ifthelightwavesconstantlychangeintime,thenthelightissaidtobe
incoherent.
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March 17, 2016 IV.
InterferencefromThinFilms:
A. Theinterferencedependsonthereflectionsandthepathlengths:
B. Thephasedifferencebetweentwowavescanchangeifoneor
bothwavesarereflected.
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March 17, 2016 C. InterferencefromThinFilms,ReflectionPhaseShifts:
1.
Forlight,whenanincidentwavetravelinginthemediumofgreater
indexofrefractionnisreflectedattheinterfaceseparatingthesecond
mediumofsmallerrefractiveindex,thereflectedwavedoesnotundergoa
changeinphase;thatis,itsreflectionphaseshiftiszero.
2.
Whenawavetravelinginamediumofsmallerindexofrefractionis
reflectedattheinterfaceseparatingthesecondmediumofahigherrefractive
index,thephasechangeisrad,orhalfawavelength.
D. Giventhebelowdrawing:
1.
Atpointaonthefrontinterface,theincidentwave(inair)reflectsfrom
themediumhavingthehigherofthetwoindexesofrefraction;sothewaveof
reflectedrayr hasitsphaseshiftedby0.5wavelength.
1
2.
Atpointbonthebackinterface,theincidentwavereflectsfromthe
medium(air)havingthelowerofthetwoindexesofrefraction;thewave
reflectedthereisnotshiftedinphasebythereflection,andthusneitheristhe
portionofitthatexitsthefilmasrayr .
2
3.
Ifthewavesofr andr aretobeexactlyinphasesothattheyproduce
1
2
fullyconstructiveinterference,thepathlength2Lmustcauseanadditional
phasedifferenceof0.5,1.5,2.5,…wavelengths.
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March 17, 2016 4.
If,instead,thewavesaretobeexactlyoutofphasesothatthereisfully
destructiveinterference,thepathlength2Lmustcauseeithernoadditional
phasedifferenceoraphasedifferenceof1,2,3,...wavelengths.
But
5.
Therefore:
E. InterferencefromThinFilms,EquationsSummary:
Note: You must draw the thin film diagram to figure out which equation to use!!!! Page
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March 17, 2016 F. InterferencefromThinFilms,Filmthicknessmuchlessthan:
G. SampleProblems(includingpracticedrawingthinfilmdiagram):
1.
Lightofwavelength624nmisincidentperpendicularlyonasoapfilm
(n=1.33)suspendedinair.Whatarethe(a)leastand(b)secondleast
thicknessesofthefilmforwhichthereflectionsfromthefilmundergofully
constructiveinterference?
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March 17, 2016 SampleProblems(continued):
2.
Aplanewaveofmonochromaticlightisincidentnormallyonauniform
thinfilmofoilthatcoversaglassplate.Thewave‐lengthofthesourcecanbe
variedcontinuously.Fullydestructiveinterferenceofthereflectedlightis
observedforwavelengthsof500and700nmandfornowavelengthsin
between.Iftheindexofrefractionoftheoilis1.30andthatoftheglassis1.50,
findthethicknessoftheoilfilm.
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March 17, 2016 SampleProblems(continued):
3.
Inthefigurebelow,twomicroscopeslidestouchatoneendandare
separatedattheotherend.Whenlightofwavelength500nmshinesvertically
downontheslides,anoverheadobserverseesaninterferencepatternonthe
slideswiththedarkfringesseparatedby1.2mm.Whatistheanglebetween
theslides?
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March 17, 2016 V.
Michelson’sInterferometer:
A. Experiment:
B. IfthematerialhasthicknessLandindexofrefractionn,thenthe
numberofwavelengthsalongthelight’sto‐and‐fropaththroughthe
materialis
C. Thenumberofwavelengthsinthesamethickness2Lofairbefore
theinsertionofthematerialis
D. Whenthematerialisinserted,thelightreturnedfrommirrorM1
undergoesaphasechange(intermsofwavelengths)of
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March 17, 2016 E. Foreachphasechangeofonewavelength,thefringepatternis
shiftedbyonefringe.Thus,bycountingthenumberoffringesthrough
whichthematerialcausesthepatterntoshift,onecandeterminethe
thicknessLofthematerialintermsofl.
F. SampleProblem:
1.
IfmirrorM2inaMichelsoninterferometer(Fig.35‐21)ismovedthrough
0.233mm,ashiftof792brightfringesoccurs.Whatisthewavelengthofthe
lightproducingthefringepattern?
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