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Dr RichardH.CyburtAssistantProfessorofPhysics
Myoffice:402cintheScienceBuilding
Myphone:(304)384-6006
Myemail:rcyburt@concord.edu
Mywebpage:www.concord.edu/rcyburt
Inpersonoremailisthebestwaytogetaholdofme.
PHYS102
MyOfficeHoursTWR9:30-11:00amW4:00-5:00pm
Meetingsmayalsobearrangedatothertimes,byappointment
PHYS102
ProblemSolvingSectionsIwouldliketohavehour-longsectionsforworkingthroughproblems.
Thiswouldbeanextracomponenttothecourseandcounttowardsextracredit
TR1-2pm
WF10-11am(NoFridaysectionthisweek!!!)
S308
Ifyoucan’tmakethese,youcanstillpickuptheproblemworksheet.
PHYS102
ThePhotonModelofElectromagneticWavesWehavelearnedthatlightisawave,butmanyexperimentsconvincinglyleadtothesurprisingresultthatelectromagneticwaveshaveaparticle-likenature.Photons aretheparticle-likecomponentoftheelectromagneticwave.
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ThePhotonModelofElectromagneticWaves
Oneexperimentthatindicatestheparticle-likebehaviorofwavesisadimphotograph.Iflightactedlikeawave,reducingitsintensityshouldcausetheimagetogrowdimmer,buttheentireimagewouldremainpresent.
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ThePhotonModelofElectromagneticWaves
Inactuality,adimphotoshowsthatonlyafewpointsonthedetectorregisteredthepresenceoflight,asifthelightcameinpieces.Whentheintensityofthelightincreases,thedensityofthedotsoflightishighenoughtoformafullpicture.
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ThePhotonModelofElectromagneticWavesThephotonmodel ofelectromagneticwavesconsistsofthreebasicpostulates:1. Electromagneticwavesconsistofdiscrete,masslessunitscalled
photons.Aphotontravelsinavacuumatthespeedoflight.
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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.
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QuickCheck25.19Aradiotoweremitstwo50Wsignals,oneanAMsignalatafrequencyof850kHz,oneanFMsignalatafrequencyof85MHz.Whichsignalhasmorephotonspersecond?
◦ TheAMsignalhasmorephotonspersecond.◦ TheFMsignalhasmorephotonspersecond.◦ Bothsignalshavethesamephotonspersecond.
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QuickCheck25.19Aradiotoweremitstwo50Wsignals,oneanAMsignalatafrequencyof850kHz,oneanFMsignalatafrequencyof85MHz.Whichsignalhasmorephotonspersecond?
◦ TheAMsignalhasmorephotonspersecond.◦ TheFMsignalhasmorephotonspersecond.◦ Bothsignalshavethesamephotonspersecond.
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Example25.9Findingtheenergyofaphotonofvisiblelight550nmistheapproximateaveragewavelengthofvisiblelight.a. Whatistheenergyofaphotonwithawavelengthof
550nm?b. A40Wincandescentlightbulb emitsabout1Jofvisiblelight
energyeverysecond.Estimatethenumberofvisiblelightphotonsemittedpersecond.
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Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)SOLVE a.Thefrequencyofthephotonis
Equation25.22givesustheenergyofthisphoton:
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Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)
Thisisanextremelysmallenergy!Infact,photonenergiesaresosmallthattheyareusuallymeasuredinelectronvolts(eV)ratherthanjoules.Recallthat1eV=1.60´ 10−19 J.Withthis,wefindthatthephotonenergyis
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Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)b. Thephotonsemittedbyalightbulb spanarangeofenergies,
becausethelightspansarangeofwavelengths,buttheaveragephotonenergycorrespondstoawavelengthnear550nm.Thuswecanestimatethenumberofphotonsin1Joflightas
Atypicallightbulb emitsabout3´ 1018 photonseverysecond.
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Example25.9Findingtheenergyofaphotonofvisiblelight(cont.)ASSESS Thenumberofphotonsemittedpersecondisstaggeringlylarge.It’snotsurprisingthatinoureverydaylifewesenseonlytheriverandnottheindividualparticleswithintheflow.
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ThePhotonModelofElectromagneticWavesDependingonitsenergy,asinglephotoncancauseamoleculartransformation(asitdoesonthesensorysystemofaneye),orevenbreakcovalentbonds.Thephotonmodeloflightwillbeessentialasweexploretheinteractionofelectromagneticwaveswithmatter.
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ThePhotonModelofElectromagneticWavesAsinglephotonoflightwithawavelengthof550nmhastheenergyof2.3eV.
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Example25.12FindingthephotonenergyforultravioletlightUltravioletradiationwithawavelengthof254nmisusedingermicidallamps.WhatisthephotonenergyineV forsuchalamp?
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Example25.12Findingthephotonenergyforultravioletlight(cont.)SOLVE ThephotonenergyisE =hf :
IneV,thisis
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Example25.12Findingthephotonenergyforultravioletlight(cont.)ASSESS Table25.1showsthatthisenergyissufficienttobreakthebondsinawatermolecule.Itwillbeenoughenergytobreakotherbondsaswell,leadingtodamageonacellularlevel.
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WhatIsLight?Undersomecircumstances,lightactslikeparticlestravelinginstraightlines,whileinothercircumstanceslightshowsthesamekindsofwave-likebehaviorassoundwavesorwaterwaves.Changethecircumstancesyetagain,andlightexhibitsbehaviorthatisneitherwave-likenorparticle-likebuthascharacteristicsofboth.
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WhatIsLight?Wedevelopthreemodelsoflight.Eachmodelsuccessfullyexplainsthebehavioroflightwithinacertaindomain.
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WhatIsLight?TheWaveModelThewavemodeloflightisthemostwidelyapplicablemodel,responsibleforthewidelyknown“fact”thatlightisawave.Itiscertainlytruethat,undermanycircumstances,lightexhibitsthesamebehaviorassoundorwaterwaves.Lasersandelectro-opticaldevices,criticaltechnologiesofthe21stcentury,arebestunderstoodintermsofthewavemodeloflight.SomeaspectsofthewavemodeloflightwereintroducedinChapters15and16,andthewavemodelistheprimaryfocusofthischapter.Thestudyoflightasawaveiscalledwaveoptics.
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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.
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ThePropagationofLightWavesAwaterwavepassesthroughawindow-likeopeninginabarrier.Thewave spreadsout tofillthespacebehindtheopening.Thisphenomenoniscalleddiffraction.Diffractionisaclearsignthatawaveispassingthroughtheopening.
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ThePropagationofLightWavesWhentheopeningismanytimeslargerthanthewavelengthofthewave,thewavecontinuestomovestraightforward.Thereisadefinedregion,the“shadow,”wherethereisnowave.Thisissimilartothestraight-lineappearanceoflightwithsharpshadowsaslightpassesthroughlargewindows.
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ThePropagationofLightWavesWhetherawavespreadsout(diffracts)ortravelsstraightaheadwithsharpshadowsoneithersidedependsonthesizeoftheobjectsthatthewaveinteractswith.Diffractionbecomesnoticeablewhentheopeningiscomparableinsizetothewavelengthofthewave.
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LightIsanElectromagneticWaveLightconsistsofveryrapidlyoscillatingelectricandmagneticfields:Itisanelectromagneticwave.
Allelectromagneticwavestravelinavacuumatthespeedoflight:
vlight =c =3.00´ 108 m/s
Visiblelightwavelengthsrangefrom400nm–700nm.Thisisthevisiblespectrum.
Becausethewavelengthsareveryshort,thefrequenciesofvisiblelightareveryhigh.Fora600nmwavelength
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TheIndexofRefractionLightwavesslowdownastheypassthroughtransparentmaterialssuchaswater,glass,orair.Thisisduetotheinteractionsbetweentheelectromagneticfieldofthewaveandtheelectronsinthematerial.Thespeedoflightinamaterialischaracterizedbythematerial’sindexofrefractionn,definedby
n isalwaysgreaterthan1becausev isalwayslessthanc.Avacuumhasn= 1.©2015PearsonEducation,Inc.
TheIndexofRefractionThefrequencyofawavedoesnotchangeasthewavemovesfromonemediumtoanother.Thereforethewavelengthmustchange.Thewavelengthoflightinamaterialis
Thewavelengthinthetransparentmaterialisshorterthanthewavelengthinavacuum.
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QuickCheck 17.1Alightwavetravels,asaplanewave,fromair(n =1.0)intoglass(n =1.5).Whichdiagramshowsthecorrectwavefronts?
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QuickCheck 17.1Alightwavetravels,asaplanewave,fromair(n =1.0)intoglass(n =1.5).Whichdiagramshowsthecorrectwavefronts?
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C.
Example17.1AnalyzinglighttravelingthroughaglassOrangelightwithawavelengthof600nmisincidentona1.00-mm-thickglassmicroscopeslide.a. Whatisthelightspeedintheglass?b. Howmanywavelengthsofthelightareinsidetheslide?
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Example17.1Analyzinglighttravelingthroughaglass(cont.)SOLVE
a. FromTable17.1weseethattheindexofrefractionofglassisnglass= 1.50.Thusthespeedoflightinglassis
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Example17.1Analyzinglighttravelingthroughaglass(cont.)b. Becausenair = 1.00,thewavelengthofthelightisthesameinair
andvacuum:lvac = lair = 600nm.Thusthewavelengthinsidetheglassis
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Example17.1Analyzinglighttravelingthroughaglass(cont.)N wavelengthsspanadistanced= Nλ ,sothenumberofwavelengthsind = 1.00mmis
ASSESS Thefactthat2500wavelengthsfitwithin1mmshowshowsmallthewavelengthsoflightare.
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TheInterferenceofLightBecauselightactsasawave,lightwavescanoverlapandinterfere constructivelyanddestructively.Weuseverysmallslitstocreatewavesthatcaninterferewitheachother.Whenthelightwavepassesthroughtheslit,itdiffracts,asuresignofwaviness.
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Young’sDouble-SlitExperimentInordertoobserveinterference,weneedtwo lightsourceswhosewavescanoverlapandinterfere.InanexperimentfirstperformedbyThomasYoungin1801,light(inourcase,alaser)isshownthroughapairofslits,adoubleslit.Lightpassingthroughtheslitsimpingesonaviewingscreen.
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Young’sDouble-SlitExperimentLightspreadsoutbehindeachslit.Aswiththesoundwaves,constructiveinterferenceoccursatapointwheredistancesr1 andr2 fromtheslitsdifferbyawholenumberofwavelengths.Constructiveinterferenceisseenasahigherintensityoflightontheviewingscreen.
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Young’sDouble-SlitExperimentDestructiveinterferencewilloccurwhenthelightwavesoccuratpositionsonthescreenforwhichr1 andr2 differbyawholenumberofwavelengthsplushalfawavelength.
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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
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AnalyzingDouble-SlitInterferenceBecausepointPisveryfarcomparedtothespacingbetweenslits,thetwopathstopointParevirtuallyparallel.
Thereforethepath-lengthdifferenceistheshortsideofthetriangle:
∆r = d sinq
Sothebrightfringesoccur:
∆r = d sinqm =ml m = 0,1,2,3,...
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AnalyzingDouble-SlitInterferenceThecenteroftheviewingscreenaty =0isequallydistantfrombothslits,soΔr =0withm =0,whichiswherethebrightestfringe(thecentralmaximum)occurs.Asyoumoveawayfromthecenter,themth brightfringeoccurswhereonewavehastraveledm wavelengthsfartherthantheotherandthusΔr =mλ.
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AnalyzingDouble-SlitInterferenceWecanusethesmallangleapproximationtorewritetheangularposition(inradians)ofthefringesas
Itismoreconvenienttomeasuretheposition ofthemth brightfringe,asmeasuredfromthecenteroftheviewingscreen:
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AnalyzingDouble-SlitInterferenceTheequationsshowthattheinterferencepatternisaseriesofequallyspacedbrightlines onthescreen.Thefringespacingbetweenfringemandfringem+1is
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AnalyzingDouble-SlitInterferenceThedarkfringesarebandsofdestructiveinterferencewherethepath-lengthdifferenceofthewavesisawholenumberofwavelengthsplushalfawavelength:
Weusetherelationshipofthepath-lengthdifferencewiththeangularseparationofthefringesfoundearlier:
∆r =d sinqm =mλ m =0,1,2,3,...
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AnalyzingDouble-SlitInterferenceCombiningthepreviousequations,wefindthatthedarkfringesarelocatedatthepositions
Thedarkfringesarelocatedexactlyhalfwaybetweenthebrightfringes.
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AnalyzingDouble-SlitInterferenceTheintensityofthelightoscillatesbetweendarkfringes,wheretheintensityiszeroandthebrightfringesareofmaximumintensity.
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QuickCheck17.2
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Thepointonthescreenmarkedwithadotishowmuchfartherfromtheleftslitthanfromtherightslit?
◦ 1.0l◦ 1.5l◦ 2.0l◦ 2.5l◦ 3.0l
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QuickCheck17.2
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Thepointonthescreenmarkedwithadotishowmuchfartherfromtheleftslitthanfromtherightslit?
◦ 1.0l◦ 1.5l◦ 2.0l◦ 2.5l◦ 3.0l
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QuickCheck17.3
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifthescreenismovedfartherawayfromtheslits,thefringeswillbe
◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Fuzzyandoutoffocus.
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QuickCheck17.3
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifthescreenismovedfartherawayfromtheslits,thefringeswillbe
◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Fuzzyandoutoffocus.
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QuickCheck17.4
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifgreenlightisused,witheverythingelsethesame,thebrightfringeswillbe
◦ Closertogether◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.
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QuickCheck17.4
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Ifgreenlightisused,witheverythingelsethesame,thebrightfringeswillbe
◦ Closertogether◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.
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dDy = lL and green light has a shorter wavelength.
QuickCheck17.5
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Iftheslitsaremovedclosertogether,thebrightfringeswillbe
◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.
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QuickCheck17.5
Alaboratoryexperimentproducesadouble-slitinterferencepatternonascreen.Iftheslitsaremovedclosertogether,thebrightfringeswillbe
◦ Closertogether.◦ Inthesamepositions.◦ Fartherapart.◦ Therewillbenofringesbecausetheconditionsforinterferencewon’tbesatisfied.
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Dy = lLd
and d is smaller.
Example17.3MeasuringthewavelengthoflightAdouble-slitinterferencepatternisobservedonascreen1.0mbehindtwoslitsspaced0.30mmapart.Fromthecenterofoneparticularfringetothecenteroftheninthbrightfringefromthisoneis1.6cm.Whatisthewavelengthofthelight?
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Example17.3Measuringthewavelengthoflight(cont.)PREPARE Itisnotalwaysobviouswhichfringeisthecentralmaximum.Slightimperfectionsintheslitscanmaketheinterferencefringepatternlessthanideal.However,youdonotneedtoidentifythem =0fringebecauseyoucanmakeuseofthefact,expressedinEquation17.9,thatthefringespacing∆y isuniform.TheinterferencepatternlookslikethephotographofFigure17.6b.
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Example17.3Measuringthewavelengthoflight(cont.)SOLVE Thefringespacingis
UsingthisfringespacinginEquation17.9,wefindthatthewavelengthis
Itiscustomarytoexpressthewavelengthsofvisiblelightinnanometers.Besuretodothisasyousolveproblems.
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