Intermediate Physics - · What Is Light? The Ray Model An equally well-known “fact” is that light travels in a straight line. These straight-line paths are called light rays.

IntermediatePhysics

PHYS102

Dr RichardH.CyburtAssistantProfessorofPhysics

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IntermediatePhysics

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DouglasAdamsHitchhiker’sGuidetotheGalaxy

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Thislecturewillhelpyouunderstand:ThePhotonModelofEMWaves

WhatisLight

TheInterferenceofLight

PHYS102

Section25.6ThePhotonModelofElectromagneticWaves

©2015PearsonEducation,Inc.

ThePhotonModelofElectromagneticWavesWehavelearnedthatlightisawave,butmanyexperimentsconvincinglyleadtothesurprisingresultthatelectromagneticwaveshaveaparticle-likenature.Photons aretheparticle-likecomponentoftheelectromagneticwave.


ThePhotonModelofElectromagneticWaves

Oneexperimentthatindicatestheparticle-likebehaviorofwavesisadimphotograph.Iflightactedlikeawave,reducingitsintensityshouldcausetheimagetogrowdimmer,buttheentireimagewouldremainpresent.


ThePhotonModelofElectromagneticWaves

Inactuality,adimphotoshowsthatonlyafewpointsonthedetectorregisteredthepresenceoflight,asifthelightcameinpieces.Whentheintensityofthelightincreases,thedensityofthedotsoflightishighenoughtoformafullpicture.


ThePhotonModelofElectromagneticWavesThephotonmodel ofelectromagneticwavesconsistsofthreebasicpostulates:1. Electromagneticwavesconsistofdiscrete,masslessunitscalled

photons.Aphotontravelsinavacuumatthespeedoflight.


ThePhotonModelofElectromagneticWavesThephotonmodel ofelectromagneticwavesconsistsofthreebasicpostulates:2. Eachphotonhasenergy:

Ephoton =hff isthefrequencyofthewaveandh istheuniversalconstant calledPlanck’sconstant:

h =6.63´ 10−34 J⋅ sInotherwords,theelectromagneticwavecomesindiscrete“chunks”ofenergyhf.©2015PearsonEducation,Inc.

ThePhotonModelofElectromagneticWavesThephotonmodel ofelectromagneticwavesconsistsofthreebasicpostulates:3. Thesuperpositionofasufficientlylargenumberofphotonshas

thecharacteristicsofacontinuouselectromagneticwave.


QuickCheck25.19Aradiotoweremitstwo50Wsignals,oneanAMsignalatafrequencyof850kHz,oneanFMsignalatafrequencyof85MHz.Whichsignalhasmorephotonspersecond?

◦ TheAMsignalhasmorephotonspersecond.◦ TheFMsignalhasmorephotonspersecond.◦ Bothsignalshavethesamephotonspersecond.


QuickCheck25.19Aradiotoweremitstwo50Wsignals,oneanAMsignalatafrequencyof850kHz,oneanFMsignalatafrequencyof85MHz.Whichsignalhasmorephotonspersecond?

◦ TheAMsignalhasmorephotonspersecond.◦ TheFMsignalhasmorephotonspersecond.◦ Bothsignalshavethesamephotonspersecond.


Example25.9Findingtheenergyofaphotonofvisiblelight550nmistheapproximateaveragewavelengthofvisiblelight.a. Whatistheenergyofaphotonwithawavelengthof

550nm?b. A40Wincandescentlightbulb emitsabout1Jofvisiblelight

energyeverysecond.Estimatethenumberofvisiblelightphotonsemittedpersecond.


Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)SOLVE a.Thefrequencyofthephotonis

Equation25.22givesustheenergyofthisphoton:


Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)

Thisisanextremelysmallenergy!Infact,photonenergiesaresosmallthattheyareusuallymeasuredinelectronvolts(eV)ratherthanjoules.Recallthat1eV=1.60´ 10−19 J.Withthis,wefindthatthephotonenergyis


Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)b. Thephotonsemittedbyalightbulb spanarangeofenergies,

becausethelightspansarangeofwavelengths,buttheaveragephotonenergycorrespondstoawavelengthnear550nm.Thuswecanestimatethenumberofphotonsin1Joflightas

Atypicallightbulb emitsabout3´ 1018 photonseverysecond.


Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)ASSESS Thenumberofphotonsemittedpersecondisstaggeringlylarge.It’snotsurprisingthatinoureverydaylifewesenseonlytheriverandnottheindividualparticleswithintheflow.


ThePhotonModelofElectromagneticWavesDependingonitsenergy,asinglephotoncancauseamoleculartransformation(asitdoesonthesensorysystemofaneye),orevenbreakcovalentbonds.Thephotonmodeloflightwillbeessentialasweexploretheinteractionofelectromagneticwaveswithmatter.


ThePhotonModelofElectromagneticWavesAsinglephotonoflightwithawavelengthof550nmhastheenergyof2.3eV.


Example25.12FindingthephotonenergyforultravioletlightUltravioletradiationwithawavelengthof254nmisusedingermicidallamps.WhatisthephotonenergyineV forsuchalamp?


Example25.12Findingthephotonenergyforultravioletlight(cont.)SOLVE ThephotonenergyisE =hf :

IneV,thisis


Example25.12Findingthephotonenergyforultravioletlight(cont.)ASSESS Table25.1showsthatthisenergyissufficienttobreakthebondsinawatermolecule.Itwillbeenoughenergytobreakotherbondsaswell,leadingtodamageonacellularlevel.


Section17.1WhatisLight?


WhatIsLight?Undersomecircumstances,lightactslikeparticlestravelinginstraightlines,whileinothercircumstanceslightshowsthesamekindsofwave-likebehaviorassoundwavesorwaterwaves.Changethecircumstancesyetagain,andlightexhibitsbehaviorthatisneitherwave-likenorparticle-likebuthascharacteristicsofboth.


WhatIsLight?Wedevelopthreemodelsoflight.Eachmodelsuccessfullyexplainsthebehavioroflightwithinacertaindomain.


WhatIsLight?TheWaveModelThewavemodeloflightisthemostwidelyapplicablemodel,responsibleforthewidelyknown“fact”thatlightisawave.Itiscertainlytruethat,undermanycircumstances,lightexhibitsthesamebehaviorassoundorwaterwaves.Lasersandelectro-opticaldevices,criticaltechnologiesofthe21stcentury,arebestunderstoodintermsofthewavemodeloflight.SomeaspectsofthewavemodeloflightwereintroducedinChapters15and16,andthewavemodelistheprimaryfocusofthischapter.Thestudyoflightasawaveiscalledwaveoptics.


WhatIsLight?TheRayModelAnequallywell-known“fact”isthatlighttravelsinastraightline.Thesestraight-linepathsarecalledlightrays.Thepropertiesofprisms,mirrors,lenses,andopticalinstrumentssuchastelescopesandmicroscopesarebestunderstoodintermsoflightrays.Unfortunately,it’sdifficulttoreconcilethestatement“lighttravelsinastraightline”withthestatement“lightisawave.”Forthemostpart,wavesandraysaremutuallyexclusivemodelsoflight.Animportanttaskwillbetolearnwheneachmodelisappropriate.Theraymodeloflight,thebasisofrayoptics,isthesubjectofthenextchapter.©2015PearsonEducation,Inc.

WhatIsLight?ThePhotonModelModerntechnologyisincreasinglyreliantonquantumphysics.Inthequantumworld,lightconsistsofphotonsthathavebothwave-likeandparticle-likeproperties.Photonsarethequantaoflight.Muchofthequantumtheoryoflightisbeyondthescopeofthistextbook,butwewilltakeapeekattheimportantideasinChapters25and28ofthistext.


ThePropagationofLightWavesAwaterwavepassesthroughawindow-likeopeninginabarrier.Thewave spreadsout tofillthespacebehindtheopening.Thisphenomenoniscalleddiffraction.Diffractionisaclearsignthatawaveispassingthroughtheopening.


ThePropagationofLightWavesWhentheopeningismanytimeslargerthanthewavelengthofthewave,thewavecontinuestomovestraightforward.Thereisadefinedregion,the“shadow,”wherethereisnowave.Thisissimilartothestraight-lineappearanceoflightwithsharpshadowsaslightpassesthroughlargewindows.


ThePropagationofLightWavesWhetherawavespreadsout(diffracts)ortravelsstraightaheadwithsharpshadowsoneithersidedependsonthesizeoftheobjectsthatthewaveinteractswith.Diffractionbecomesnoticeablewhentheopeningiscomparableinsizetothewavelengthofthewave.


LightIsanElectromagneticWaveLightconsistsofveryrapidlyoscillatingelectricandmagneticfields:Itisanelectromagneticwave.

Allelectromagneticwavestravelinavacuumatthespeedoflight:

vlight =c =3.00´ 108 m/s

Visiblelightwavelengthsrangefrom400nm–700nm.Thisisthevisiblespectrum.

Becausethewavelengthsareveryshort,thefrequenciesofvisiblelightareveryhigh.Fora600nmwavelength


TheIndexofRefractionLightwavesslowdownastheypassthroughtransparentmaterialssuchaswater,glass,orair.Thisisduetotheinteractionsbetweentheelectromagneticfieldofthewaveandtheelectronsinthematerial.Thespeedoflightinamaterialischaracterizedbythematerial’sindexofrefractionn,definedby

n isalwaysgreaterthan1becausev isalwayslessthanc.Avacuumhasn= 1.©2015PearsonEducation,Inc.

TheIndexofRefraction


TheIndexofRefractionThefrequencyofawavedoesnotchangeasthewavemovesfromonemediumtoanother.Thereforethewavelengthmustchange.Thewavelengthoflightinamaterialis

Thewavelengthinthetransparentmaterialisshorterthanthewavelengthinavacuum.


QuickCheck 17.1Alightwavetravels,asaplanewave,fromair(n =1.0)intoglass(n =1.5).Whichdiagramshowsthecorrectwavefronts?


QuickCheck 17.1Alightwavetravels,asaplanewave,fromair(n =1.0)intoglass(n =1.5).Whichdiagramshowsthecorrectwavefronts?


C.

Example17.1AnalyzinglighttravelingthroughaglassOrangelightwithawavelengthof600nmisincidentona1.00-mm-thickglassmicroscopeslide.a. Whatisthelightspeedintheglass?b. Howmanywavelengthsofthelightareinsidetheslide?


Example17.1Analyzinglighttravelingthroughaglass(cont.)SOLVE

a. FromTable17.1weseethattheindexofrefractionofglassisnglass= 1.50.Thusthespeedoflightinglassis


Example17.1Analyzinglighttravelingthroughaglass(cont.)b. Becausenair = 1.00,thewavelengthofthelightisthesameinair

andvacuum:lvac = lair = 600nm.Thusthewavelengthinsidetheglassis


Example17.1Analyzinglighttravelingthroughaglass(cont.)N wavelengthsspanadistanced= Nλ ,sothenumberofwavelengthsind = 1.00mmis

ASSESS Thefactthat2500wavelengthsfitwithin1mmshowshowsmallthewavelengthsoflightare.


Section17.2TheInterferenceofLight


TheInterferenceofLightBecauselightactsasawave,lightwavescanoverlapandinterfere constructivelyanddestructively.Weuseverysmallslitstocreatewavesthatcaninterferewitheachother.Whenthelightwavepassesthroughtheslit,itdiffracts,asuresignofwaviness.


Young’sDouble-SlitExperimentInordertoobserveinterference,weneedtwo lightsourceswhosewavescanoverlapandinterfere.InanexperimentfirstperformedbyThomasYoungin1801,light(inourcase,alaser)isshownthroughapairofslits,adoubleslit.Lightpassingthroughtheslitsimpingesonaviewingscreen.


Young’sDouble-SlitExperimentLightspreadsoutbehindeachslit.Aswiththesoundwaves,constructiveinterferenceoccursatapointwheredistancesr1 andr2 fromtheslitsdifferbyawholenumberofwavelengths.Constructiveinterferenceisseenasahigherintensityoflightontheviewingscreen.


Young’sDouble-SlitExperimentDestructiveinterferencewilloccurwhenthelightwavesoccuratpositionsonthescreenforwhichr1 andr2 differbyawholenumberofwavelengthsplushalfawavelength.


Young’sDouble-SlitExperimentAlongtheviewingscreen,thedifferenceΔr alternatesbetweenbeingawholenumberofwavelengthsandawholenumberofwavelengthsplushalfawavelength,leadingtoaseriesofalternatingbrightanddarkbandsoflightcalledinterferencefringes.Thecentralmaximum isthebrightestfringeatthemidpointofthescreen.©2015PearsonEducation,Inc.

AnalyzingDouble-SlitInterferenceThedoubleslitexperimentconsistsofadoubleslitspacedd apartandadistanceL totheviewingscreen.WeassumeL isverymuchlargerthand.Constructiveinterferenceoccurswhen∆r =ml m = 0,1,2,3,...

Itproducesabrightfringeatthatpoint.©2015PearsonEducation,Inc.

AnalyzingDouble-SlitInterferenceWemustfindthepositionsonthescreenwhereΔr =mλ.PointPonthescreenisadistancey fromthecenteroftheviewingscreen,oranangleq fromthelineconnectingthecenteroftheslittothecenterofthescreen.Theyarerelated:

y = L tanq


AnalyzingDouble-SlitInterferenceBecausepointPisveryfarcomparedtothespacingbetweenslits,thetwopathstopointParevirtuallyparallel.

Thereforethepath-lengthdifferenceistheshortsideofthetriangle:

∆r = d sinq

Sothebrightfringesoccur:

∆r = d sinqm =ml m = 0,1,2,3,...


AnalyzingDouble-SlitInterferenceThecenteroftheviewingscreenaty =0isequallydistantfrombothslits,soΔr =0withm =0,whichiswherethebrightestfringe(thecentralmaximum)occurs.Asyoumoveawayfromthecenter,themth brightfringeoccurswhereonewavehastraveledm wavelengthsfartherthantheotherandthusΔr =mλ.


AnalyzingDouble-SlitInterferenceWecanusethesmallangleapproximationtorewritetheangularposition(inradians)ofthefringesas

Itismoreconvenienttomeasuretheposition ofthemth brightfringe,asmeasuredfromthecenteroftheviewingscreen:


AnalyzingDouble-SlitInterferenceTheequationsshowthattheinterferencepatternisaseriesofequallyspacedbrightlines onthescreen.Thefringespacingbetweenfringemandfringem+1is


AnalyzingDouble-SlitInterferenceThedarkfringesarebandsofdestructiveinterferencewherethepath-lengthdifferenceofthewavesisawholenumberofwavelengthsplushalfawavelength:

Weusetherelationshipofthepath-lengthdifferencewiththeangularseparationofthefringesfoundearlier:

∆r =d sinqm =mλ m =0,1,2,3,...


AnalyzingDouble-SlitInterferenceCombiningthepreviousequations,wefindthatthedarkfringesarelocatedatthepositions

Thedarkfringesarelocatedexactlyhalfwaybetweenthebrightfringes.


AnalyzingDouble-SlitInterferenceTheintensityofthelightoscillatesbetweendarkfringes,wheretheintensityiszeroandthebrightfringesareofmaximumintensity.


QuickCheck17.2

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Thepointonthescreenmarkedwithadotishowmuchfartherfromtheleftslitthanfromtherightslit?

◦ 1.0l◦ 1.5l◦ 2.0l◦ 2.5l◦ 3.0l


QuickCheck17.2

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Thepointonthescreenmarkedwithadotishowmuchfartherfromtheleftslitthanfromtherightslit?

◦ 1.0l◦ 1.5l◦ 2.0l◦ 2.5l◦ 3.0l


QuickCheck17.3

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifthescreenismovedfartherawayfromtheslits,thefringeswillbe

◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Fuzzyandoutoffocus.


QuickCheck17.3

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifthescreenismovedfartherawayfromtheslits,thefringeswillbe

◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Fuzzyandoutoffocus.


QuickCheck17.4

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifgreenlightisused,witheverythingelsethesame,thebrightfringeswillbe

◦ Closertogether◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.


QuickCheck17.4

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifgreenlightisused,witheverythingelsethesame,thebrightfringeswillbe

◦ Closertogether◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.


dDy = lL and green light has a shorter wavelength.

QuickCheck17.5

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Iftheslitsaremovedclosertogether,thebrightfringeswillbe

◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.


QuickCheck17.5

Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Iftheslitsaremovedclosertogether,thebrightfringeswillbe

◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.


Dy = lLd

and d is smaller.

Example17.3MeasuringthewavelengthoflightAdouble-slitinterferencepatternisobservedonascreen1.0mbehindtwoslitsspaced0.30mmapart.Fromthecenterofoneparticularfringetothecenteroftheninthbrightfringefromthisoneis1.6cm.Whatisthewavelengthofthelight?


Example17.3Measuringthewavelengthoflight(cont.)PREPARE Itisnotalwaysobviouswhichfringeisthecentralmaximum.Slightimperfectionsintheslitscanmaketheinterferencefringepatternlessthanideal.However,youdonotneedtoidentifythem =0fringebecauseyoucanmakeuseofthefact,expressedinEquation17.9,thatthefringespacing∆y isuniform.TheinterferencepatternlookslikethephotographofFigure17.6b.


Example17.3Measuringthewavelengthoflight(cont.)SOLVE Thefringespacingis

UsingthisfringespacinginEquation17.9,wefindthatthewavelengthis

Itiscustomarytoexpressthewavelengthsofvisiblelightinnanometers.Besuretodothisasyousolveproblems.


ExampleProblemTwonarrowslits0.04mmapartareilluminatedbylightfromaHeNelaser(λ =633nm).Whatistheangleofthefirst(m =1)brightfringe?Whatistheangleofthe30th brightfringe?


Intermediate Physics - · What Is Light? The Ray Model An equally well-known “fact” is that light travels in a straight line. These straight-line paths are called light rays.

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