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CBSEClass12Physics

RevisionNotes

Chapter-10

WaveOptics

Wavefront:Itisthecontinuouslocusofallsuchparticlesofthemediumwhichare

vibratinginthesamephaseofoscillationatanyinstant.

Dependingupontheshapeofthesourceoflight,wavefrontareofdifferentshapes.

(i)Planewavefront

(ii)Sphericalwavefront

(iii)Cylindricalwavefront

Rays:Raysarethearrowsperpendiculartothewavefrontinthedirectionof

propagationofawave.

TimeTaken:Thetimetakenforlighttotravelfromonewavefronttoanotheris

calledtimetakenbyaray.

Huygens’Principle:

1. AccordingtoHuygens’Eachpointonthegivenwavefront(calledprimarywavefront)

actsasafreshsourceofnewdisturbance,calledsecondarywavelet,whichtravelsinall

directionswiththevelocityoflightinthegivenmedium.

2. Asurfacetouchingthesesecondarywavelets,tangentiallyintheforwarddirectionatany

instantgivesthenewwavefrontatthatinstant.Thisiscalledsecondarywavelets.

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PrincipleofHuygens’Construction:

1. Itisbasedontheprinciplethateverypointonawavefrontisasourceofsecondary

wavefront.

2. Theenvelopeofthesewavefrontsi.e.,thesurfacetangenttoallthesecondarywavefront

givesthenewwavefront.

Snell’slawofrefraction:

ReflectionofPlaneWavesUsingHuygens’Principle:Thelawofreflection(i=

r)canbederivedusingthewavetheory.

RefractionofPlaneWavesUsingHuygens’Principle:theSnell’slawofrefraction

canbederivedusingthewavetheory.(Herev1andv2are

thespeedoflightinmedia1and2withrefractiveindex and respectively).

RelationbetweenFrequencyandSpeed:Thefrequency remainsthesameaslight

travelsfromonemediumtoanother.Thespeedvofawaveisgivenby

Where isthewavelengthofthewaveand istheperiodofoscillation.

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DopplerEffect:Wheneverthereisarelativemotionbetweenthesourceand

observerthentheapparentfrequencyofligtreceivedbytheobserverisdifferent

fromtheactualfrequencyemittedbythesourceoflight.ThiseffectiscalledDoppler's

effectinlight.Theeffectcanbeusedtomeasurethespeedofanapproachingor

recedingobject.

ChangeinFrequency:Forthesourcemovingawayfromtheobserver ,and

forthesourcemovingtowardstheobserver ,.Thechangeinfrequencyis

So,finally,

CoherentandIncoherentAdditionofWaves:

Coherentsources:-Twosourcesoflightwhichcontinouslyemitlightwavesofsame

frequency(orwavelength)withazeroorconstantphasedifferencebetweenthem,

arecalledcoherentsources.

Incoherentsources:-Twosourcesoflightwhichdonotemitlightwaveswitha

constantphasedifferencearecalledincoherentsources.

ThetotalintensityIisnotjustthesumofindividualintensitiesI1andI2duetothetwo

sourcesbutincludesaninterferenceterm-

Theinterferencetermaveragedovermanycyclesiszeroif

1. Thesourceshavedifferentfrequenciesor

2. Thesourceshavethesamefrequencybutnostablephasedifference.

3. Forsuchcoherentsources-

4. Accordingtothesuperpositionprinciplewhentwoormorewavemotionstraveling

throughamediumsuperimposeoneanother,anewwaveisformedinwhichresultant

displacementsduetotheindividualwavesatthatinstantisgivenby-

5. Theaverageofthetotalintensitywillbe

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Where istheinherentphasedifferencebetweenthetwosuperimposingwaves.

6. Thesignificanceisthattheintensityduetotwosourcesoflightisnotequaltothesumof

intensitiesduetoeachofthem.

7. Theresultantintensitydependsontherelativelocationofthepointfromthetwosources,

sincechangingitchangesthepathdifferenceaswegofromonepointtoanother.

8. Asaresult,theresultingintensitywillvarybetweenmaximumandminimumvalues,

determinedbythemaximumandminimumvaluesofthecosinefunction.Thesewillbe

=

=

Young’sExperiment

TwoparallelandverycloseslitsS1andS2(illuminatedbyanothernarrowslit)behave

liketwocoherentsourcesandproduceapatternofdarkandbrightbandsonascreen

knownasinterferencefringes.

ForapointPonthescreen,thepathdifference

Wheredistheseparationbetweentwoslits,Disthedistancebetweentheslitsand

thescreenandxisthedistanceofthepointofPfromthecentralfringe.

Forconstructiveinterference(brightband),thepathdifferencemustbeaninteger

multipleof ,i.e.-

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Theseparation betweenadjacentbright(ordark)fringesis, usingwhich

canbemeasured.

Young’sDoubleSlitInterferenceExperiment:Fringewidth,

whereDisthedistancebetweentheslits&thescreendisthedistancebetweenthe

twoslits

ConstructiveInterference:

1. Phasedifference: wherenisaninteger

2. Pathdifference: wherenisaninteger

Destructiveinterference:

1. Phasedifference: ,wherenisaninteger

2. Pathdifference: ,wherenisaninteger

Intensitydistributioncurveforinterference:

Interferencefringeswithwhitelight:-Whentheslitsareilluminatedwithwhite

light,theinterferencepatternconsistofacentralwhitefringehavingonbothsidesa

fewcolouredfringesandthenageneralillumination.

Conditionsforsustainedinterference:-

(i)Twosourcesoflightmustbecoherent.

(ii)Thefrequencies(orwavelength)ofthetwowavesshouldbeequal.

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(iii)Thelightmustbemonochromatic.

(iv)Theamplitudesoftheinterferingwavesmustbeequalornearlyequal.

(v)Thetwosourcesmustbenarrow.

Diffraction:

Thephenomenonofbendingoflightaroundthecornersofanobstacleiscalledthe

diffractionoflight.

DiffractionduetoSingleSlit:

1. Thesingle-slitdiffractionpatternshowsthecentralmaximum ,zerointensity

atangularseparation

2. Angularspreadofthecentralmaxima

3. Widthofthecentralmaxima:

WhereDisthedistanceoftheslitfromthescreen,distheslitwidth.

ConditionfortheMinimaontheeithersideoftheCentralMaxima: ,

wheren=1,2,3,….

Relationbetweenphasedifference&pathdifference:

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Where isthephasedifference& isthepathdifference.

DifferentPartsoftheWaveFrontattheSlitactasSecondarySources:

1. Diffractionpatternistheresultofinterferenceofwavesfromthesesources.

2. Theintensityplotlooksasfollows,withtherebeingabrightcentralmaximum,followed

bysmallerintensitysecondarymaxima,withtherebeingpointsofzerointensityin

between,whenever

3. Widthofcentralmaximumisdirectlyproportionaltowavelengthoflightandinversely

proportionaltothewidthoftheslit.

Emission,AbsorptionandScattering:

1. Thesearethethreeprocessesbywhichmatterinteractswithradiation.Inemission,an

acceleratedchargeradiatesandlosesenergy.

2. Inabsorption,thechargegainsenergyattheexpenseoftheelectromagneticwave.

3. Inscattering,thechargeacceleratedbyincidentelectromagneticwaveradiatesinall

direction.

Polarization:

1. Ifthevibrationsofawavearepresentinjustonedirectioninaplaneperpendicularto

thedirectionofpropagation,thewaveissaidtobepolarisedorplanepolarised.the

phenomenonofrestrictingtheoscillationsofawavetojustonedirectioninthe

transverseplaneiscalledpolarisationofwaves.

2. WhenlightpassesthroughasinglepolaroidP1lightintensityisreducedtohalf,

independentoftheorientationofP1.WhenasecondPolaroidP2isalsoincluded,atone

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specificorientationw.r.tP1,thenettransmittedintensityisreducedtozerobutis

transmittedfullywhenP1isturned900fromthatorientation.Thishappensbecausethe

transmittedpolarizationbyapolaroidisthecomponentofEparalleltoitsaxis.

3. Polariser:Adevicethatpolarisestheunpolarisedlightpassedthroughitiscalleda

polariser.

4. Unpolarizedsunlightscatteredbytheatmosphereorreflectedfromamediumgets

partiallypolarized.

OpticalActivity:Whenplanepolarisedlightpassesthroughacertainsubstances,the

planeofpolarisationofthelightisrotatedaboutthedirectionofpropagationoflight

throughacertainangle.Thisphenomenoniscalledopticalactivityoropticalrotation

andthesubstancesopticallyactive.

IntensityoftheLightduetoPolarization(LawofMalus):

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WhereIistheintensityoflightafterpolarization,Ioistheoriginalintensity, isthe

anglebetweentheaxisoftheanalyzer&thepolarizer

AgraphbetweentheintensityoflightItransmittedbytheanalyserandtheangle

betweenthepolariserandtheanalyserwillbeasshown-

Methodsofproducingplanepolarisedlight:

1. Reflection

2. Scattering

3. Doublerefraction

Polarisationbyreflection(Brewster’sLaw):Whenunpolarisedlightisincidentona

transparentsurfaceatthepolarisingangle ,thereflectedlightispolarisedwithits

electricvectorperpendiculartotheplaneofincidencewhentherefractedand

reflectedraysmakearightanglewitheachother.

PolarizationbyScattering:

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1. Lightisscatteredwhenitmeetsaparticleofsimilarsizetoitsownwavelength.The

scatteringofsunlightbydustparticlesisanexampleofpolarizationbyscattering.

Polarizationbydoublerefraction:Whenanunpolrisedraypassesthroughcertain

crystalslikequartzorcalcite,itspiltsupintotworays.Thisphenomenoniscalled

doublerefraction.

Rayleighshowedthatthescatteringoflightisproportionaltothefourthpowerofthe

frequencyofthelightorvariesas where isthewavelengthoflightincidenton

theairmoleculesofsize‘d’where .Hencebluelightisscatteredmorethan

red.Thisexplainsthebluecolourofthesky.

Polaroids:Polaroidsarethincommercialsheetswhichmakeuseofthepropertyof

selectiveabsorptiontoproduceanintensebeamofplanepolarisedlight.

Usesofpolaroids-Insunglassesandcamerafilters,Inwindscreens,Inwindow

panesofaeroplanes,InLCDsetc.