《大學(xué)物理簡明教程》 課件 9-2 Wave Optics

WaveOpticsInterferenceDiffractionTwo-slitinterferencesingle-slitcircularaperturediffractiongratingGeneralprincipalofwaveinterferencein2D(or3D)PSourceSourceS1SourceS2Sphericalwaveinphaseinphaseor

outofphase??

S1S2

PAtPointPTheamplitudeofthenetoscillationatthepointP:

=2k

(inphase)(2k+1)

(outofphase)constructiveinterferencedestructiveinterference

=k

(inphase)(k-1/2)

(outofphase)Forelectromagneticwaves:differenceofopticalpath

(n2r2-n1r1)Whydoweuseopticalpath

?Geometriclengthrn=13wavelengthsn'=26wavelengths

Twicethephasechange!thephasechangeisdeterminedbytheopticalpathlengthopticalpathlength=nr

=

ropticalpathlength=n’r

=

2r

wavelengthinvacuum

Huygens’sPrincipleChristianHuygens(1629-1695)DutchphysicistStatement:

Everypointonawave-frontmaybeconsideredasourceofsecondarysphericalwaveletswhichspreadoutintheforwarddirection.Thenewwave-frontisthetangentialsurfacetoallofthesesecondarywavelets.PlanarwaveSphericalwaveThomasYoung

(13June1773

–10May1829)wasanEnglish

polymathandphysician.Young’sdouble-slitexperiment….firstestablishedtheundulatorytheoryoflight,andfirstpenetratedtheobscuritywhichhadveiledforagesthehieroglyphsofEgypt.

…

-Young’sepitaphTheRosettastoneYoung’sdouble-slitexperimentYoung’sdouble-slitexperimentm=0m=+1m=-1m=+2m=-2Theopticalpathdifference:If(forexample,D=1m,s=10-4m)Thenumbermisanintegercalledtheordernumber.Thecentralbrightfringeat(θ

=0)isassociatedwiththem=0andiscalledthezeroth-ordermaximum.Thefirstmaximumoneitherside,forwhichm=1,iscalledthefirst-ordermaximum.m=2,second-ordermaximum.......1.TheconditionsforbrightanddarkfringesTheconditionforbrightfringesatPis:

(constructive

interference)Theseequationsprovidetheangular

positionsθ

ofthefringes.m=1,first-orderminimum

m=2,second-orderminimum.......TheconditionfordarkfringesatPis:

(destructive

interference)Brightfringes

Darkfringes

thedarkfringesmeasuredfromOareatActually,wehave:D>>s

ands>>λthebrightfringesmeasuredfromOareatThedistancesbetweentheadjacentbrightfringes(darkfringes)areequal.Fringesformedbythewhitelightm=0m=+1m=-1S*ExampleWhenwhitelightisusedinthedouble-slitexperiment,wemayseespread-outspectraofdifferentcolorsatbrightfringes.Pleasefindoutthehighestorderofthebrightfringethatisnotoverlappedbyanotherbrightfringe0th(n+1)thnth1stnthbrightfringeofredoverlapswith(n+1)th

brightfringeofviolet

Onlythefirst-orderbrightfringe!ExampleAmonochromaticlightisusedinthedouble-slitexperiment.Thewavelengthis0.6um.The4thorderbrightfringeisatpointP.WhentheslitS1iscoveredbyapieceofglasswiththeindexofrefractionof1.5,thezeroth-orderbrightfringeshiftstothepointP.Findthethicknessoftheglass.4thbrightzerothbrightThebendingoflightaroundthecornersofanobstacleorapertureintotheregionofgeometricalshadowoftheobstacle.PoissonspotSmallcircularapertureDiffraction“thebendingoflightaroundanobstacle”Geometricaloptics(nodiffraction)waveoptics(diffraction)*SscreenobstacleFraunhoferDiffractionIfthereisnodiffraction,whatwillyouseeonthescreen?fOP

Opticallensdoesnotcausedifferenceonopticalpathlength(OPL)123123

DiffractionaftertheslitfOPAbB

C*SLightfromentireslitarrivesatO

inphase.--centralbrightband.lightintensityatPisdeterminedbytheopticalpathdifferencebetweenthetworaysemittedfromtheedgesoftheslit(AandB).diffractionangle.2

2

2

ABb

C1.Drawaseriesofparallelplanes

todivide

BC(bsin

)intoseveralshortsegmentsofequallength/2,andsimultaneouslydividetheslitintoseveralnarrowstripsofequalwidth.2.lightraysoftwoadjacentstripswillcancelouteachotherduetothepathdifferenceof/2.-destructiveinterferenceoccurs.11’22’33’Whatkindofinterferencewillhappenbetweenrays1and1’?b1′2BAHalf-wavezone12′λ/2

=bsin=2×

/2

Whatwillhappenifthereisonlytwosuchstrips?Darkfringeatangle

thatsatisfiessin=/b

Darkfringe!

howabout4,6,8…strips?howabout3,5,7…strips?Comparewithdouble-slit?2

2

2

ABa

C1I/I0

/b-(

/b)2(

/b)-2(

/b)0sin

IntensityofFringes

or

………1I/I0

/b-(

/b)2(

/b)-2(

/b)0sin

IntensityofFringesThewidthsofallnonzeroorderbrightfringesareequal.Thewidthofthecentralbrightfringeistwotimesofthewidthofotherbrightfringes.Theangularwidthofcentralbrightfringe:Theangularwidthofotherordersbrightfringe:Smallangleapproximationssin

;tg

Comparisonbetweendouble-slitandsingle-slitpatternsCentralbrightfringewidthdouble-slitpatternbrightdarksingle-slitpatterndarkbrightcenter

DiffractionSpectrumFresnelsingleslitdiffraction(Assumethewavelengthis600nm)Diffraction:CircularApertureS*Fraunhoferdiffractionset-upTheangularradiusofthefirstdarkring:aperturediameterangleinradiansAirydiskAngularResolutionWhatisthesmallestangulardistancebetweentwoobjects,sothatwecandistinguishthem?(Resolution)Rayleigh’sCriterionforResolutionTwopointsourcesareregardedasjustresolvedwhentheprincipaldiffractionmaximumofoneimagecoincideswiththefirstminimumoftheother.resolvedcriticalsituation-justresolvedcan‘tdistinguishthethem....ResolutionPower(minimumangletoberesolved)Increasingthediameteroftheaperturemillimetercentimeter-decimeter2metersUsingashorterwavelengthvioletlight,ultraviolet,X-ray,electrons(matterwave)TheDiffractionGratingA

diffractiongrating

isanopticalcomponentwithaperiodicstructure,whichsplitsand

diffracts

lightintoseveralbeamstravellingindifferentdirections.

abSL1LensL2GratingFraunhoferdiffractionset-upYIGratingLensViewingScreenb，thedistancebetweenneighboringslits.a，thewidthofafineslitd,thegratingconstantSupposethegratinghasNslitsinlengthl,thendloPfGL

dsin

d

Allthelightraystravellingattheangle

willbeconvergedatpointP–onthefocalplane,alsotheviewingscreen.BrightnessatP–thesuperpositionofallthelightsN-slitinterference!InterferenceofmanysingleslitsG

dsin

d

TheopticalpathdifferencebetweenwavesfromtwoadjacentslitsisequaltoThecorrespondingphasedifferenceisEachslitactsasasourceofwave,andtheyareinphaseattheslits.Therefore,theresultantlightatPisthesuperpositionofNharmonicoscillations(Efield&Bfield)withsamefrequencyandsameamplitude.Theirphasedifference(onebyone)is………

dsin

d

IfandA=?brightnessBrightfringesDarkfringesIfandthenA＝0sin

I04-8-4(

/d)Diffractiongratingpattern(fringes)Question–N=?Darkfringes

Example:N＝?IN2I0

dsin

λ12-1-2-303theintensityofeachmainbrightfringesisnotuniform!sin

0II0-2-112(

/a)IN2I0048-4-8sin

(

/d)sin

N204-8-48(

/d)envelopeSingle-slitIncreasingthenumberofslitsSingle-slitspectrumN-slitspectrumTheequationofdiffractiongrating(brightfringes)AngularpositionproportionaltothewavelengthDifferentwavelengthscanbedistinguishedathighorderbrightfrin