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Chapter 3 Waves（第1页）

Chapter3Waves

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Chapter2exploredtheideaoflightasgoffuicles，movingalorajectories.This‘billiardball’model，inwhichalightbeamisaofindividual，padwell-localizedbuandsintrasttothealternativeview，whichisthatlightisawave.Thisoflighthasbeenpursuediheparticleviewoflight，althoughittookmanyyearsofdisdexperimentationfortheiefullyaccepted.

Unexplainedphenomena?

Otherobservations，suadebyFranaldiihtury，graduallyaccruedevidedidnotfitwiththepartialdisawthatlightraysdeviatedfrhtliheypassedthroughsmallapertures，suchasatinyholeiedthatthelightwasdiffusedandthattheedgesofthebeamwerefrihcolour，especiallypronounallobjectssuchasahairorapieceofgauze.Hecludedthatthestriationsseewasionasmallornarrowobjectwereevidehelighthadbeefrinalpathasitpassedtheedgesoftheseobjects.Iflightreallysistedofpartigalhtrays，suchsolidobjectswouldsurelyjustcastashadow，andparticlestodeviateintepatterns.

Further，theproblemtonandhisporariesofthebizarrewayinwhichlightwasrefractedthroughmaterials，notablycrystalssuchascalaturallymineral—dedexplanationintermsofsimplepartiexampleofthisbehaviourisshownihewHT，writteofpaper，isilluminatedbyalightbulb.Twopiecesofcalcitehavebeenplacedovereachhalf.IhalfofFigure15（a），twoimagesofthelacedwithrespecttoeachother.Ihalf，thetwoimagesaredisplatheoppositedire.Theleihalfandtheupperiarejustasofromordiionoflightreflethepaper，seenthroughthecrystal.Buttheseagesappearstoariseasiffromadiffereiveindex.Byplagapolarizeroverthecrystal，asshowninFigure15（b）and15（c），itispossibletoisolateimagesformedbytwodiffereionsht.Eachpolarizationexperiencesadiffereiveihisisthephenomenence.

15.AnillustratieheimageHTviewedthroughapairofcalcitecrystals，usinga.u，b.verticallypht，andtallypht.

&ionsallpoiuresoflightthatdemaion.Theyarekivelyasinterfereion，andpolarization.Wewillexplorethesephehischapter，developingapictureoflightaswavemotion.

&handwavefrequency

Whatarethecharacteristiotion?Wavesareaformofundulationassociatedwithamedium，forexamplewaterwavesonthesurfaceofapond.Thesewavessistoftheup-and-downmotionofwatermoleculesattheiweentheliquidahehighestasofthismotiohepeaksandtroughsofthehilethewaveitselfmovesacrossthesurface—thatis，atrightahemotioermolecules.Forthisreasonitiscalledatrasspeeddepehofthewater，ams.

Thecircularsurfacewavesthatradiateawayfromthepointatwhieistothewater，asshowninFigure16a，areafamiliareffect.Thedistaweensuccessivepeaksiscalledthewavelength（Figure16b），awhichpeakshittheshoreiscalledthefrequency（Figure16c）.Theproductofthesetwoquahespeedofthe>

Thepuzzleformaurieswaswhatkindofundulationsstitutedlight.Itwasassumedthatsomemediumwouldiosupportawave.Ahespeedoflightisse，thiswouldobeaverystiffmedium.Butastiffmediumwouldsurelymakeitdifficultforotherbodiesthit.Forinstance，becauseweseedistantstars，thereshouldsurelybesomemediumtosuppationoflightbetweehaar.Sihmovesarouheplawouldbeuallysweptbya‘wind’asittravelledthroughsuchamedium.Thisenigmaticmediumwascalledthe‘aether’，anditwasnotuhe19thturythatitwasfinallydiscardedasausefulcept.

16.Acircularwaveonawatersurfatoursofequalheight，calledwavefronts，b.waveheightvsdistantreatapartistant，c.waveheightvstimeataparticularlo.

So，whatsortofwaveislight?Thiswasalsofinallyahe19thturybyJamesClerkMaxedthatitisanosofanewkiheeleaghisfieldiseffectivelyaforcethataelectricdmagerials.Forexample，acledwithstaticelectricityartiagwillbeattractedtothederator.Iercaseyoufeelthisforceasyouplacethemaghedowardsthedoorunlessanopposingforceissupplied.

Inbothcases，aforcepullsoheother，sothatatsomedistanceawayfromthecloththedustparticlefeelsthisforceduetotheelectricfieldgehethedsimilarlyferatordoor，duetothemagicfieldgehemagheearly19thtury，MichaelFaradayhadshowntheesbetweerieticfields.Maxwellbroughtthemtogether，astheeleagicforcefield.Itturnsoutthatinthewavemodel，lightsideredasveryhighfrequencyossoftheeleagicfield.Oneceofthisideaisthatmoviricchargeseratelightwaves.I’lldiscussthis，ahlight，inChapter5.

Interference

Iftwostonesaredroppediooheresultisofexpandingcircularwavescollide.Someofthepeaksaretherefher，wherethewavesreiher.Buttherearealsoliwater，wherethereisnoup-and-dowhewatersurfathoughthewavesgehstourbaerarepassingthroughallpointsaloheloofsuesisshowninFigure17，alongwiththewavefronts—thelocusofpointsohewavesemanatingfromeachsource.

17.a.Twcircularwavesonawatersurface.Thedashedlioursofequalphase.b.struterferehsofequallength.c.Destruterferehsdiferingbyhalfawavelength.

Thisphenomenonisknownasinterferearisesfromtheadditioudeofthehepeaksofthetwowavescide，theresultiwicethesize，oramplitude，ofeitherwave.Thewavesaresaidtobeiheinterfereructive.ThisisshowninthemiddlediagramofFigure17.If，however，thewavesareexactlyoutofphase，sothatthepeaksofonecidewiththetroughsoftheother，thelitudeofzero:thewaveshave‘eaerfereddestructively.Thisisshowure17.Itisimmediatelyclearthatsuenonothappenwithparticles，forhowcouldtwopartiother?

ItwastheobservationofinterferesinafamousexperimentbyThomasYoungin1803thatreallyputtheictureoflightastheleadingdidateasaioureoflight.Youwasverysimple，a.Hetookadleasalightsourdplaceditbehindaswhichthereweretwoholesaverysmalldistahelightshiningthroughtheseholescouldbeseenonasedsedistanow，ifonlyasingleholewasused—saybygupthesethelightmadeasionthes.Whenbothholeswereopehingmarvelloushappeeadofjustaspotoftwicethebrightnowhadstriations.Thesearegeraightliensityperpendiculartothelinejoireofthetwospots，asshowniioninFigure18arisingfromtheiheassingthroughthetwoholes.Theyarecalled‘Yes’，ahekeypiecesofevidencefhtasawavemotion.

Howdoesinterfereheces’observedbyoionsfromtwosurfacesveryclosetogether?Whatiserfereooccuristwowaves，therelativephaseofwhich（thatis，therelativepositionsofthepeaksofthetwowaves）beadjusted.Io，interferenceoccursbecauseasibeamoflightispartiallyreflectedatthetwosurfadthussplitintotwowaves.Ifthedistawosurfacesisequaltoasihofthelight，thehetworeflectedwavesdthereisabrightfringe.If，however，thedistahalfofthewavelehepeakofohthetroughofthesedthereisa‘darkfriodestruterferehus，whenyoulookatthesurfacethebrightanddarkfrithetoursoftheseparationofthesurfacewitharesolutiohah.Fht，withawavelengthofapproximatelyone-halfofamillionthofametre，or500ioermihan250nm—apreofabout140thofthediameterofahumanhair.

18.ThomasYouhelightfromoproducesasmoothiterhslitsarees’appear，characteristicofwave-likebehaviour.

Ofcourse，foradifferehebrightanddarkfringeswilloadifferethesurfaceshesofcolourwhenillumihwhitelight.Itisinterferewavesthatcausestheathinfilmofoilfloatingon>

Iransformsverysmalldistaheorderofthewavelengthoflight，intlightiy—fromnolighttofourtimesasbrightastheindividualtwaves.Sugesiyareeasytodetectorsee，andthusinterferenceisaverygoodwaytomeasuresmalldisplathescaleofthewavelengthoflight.Manyoptisorsarebasedoninterferes.

Holography

Interfereneansbywhiaketrue3Dimages，thatis，imagesthatbeviewedfrlesandrevealdiffereheobject.Thesearediffereicimagesinso-called3Dfilms，andares.Hologramsaremadebyregthefullwavefhtscatteredfromahesortof2Dimageswe’reusedtraphyeheamplitudeofthewaves.Thephaseinformationislost.Thisisbecausedetelyrespondtoamplitude，sothereisnowayisofimageswehavelookedatpreviouslytoextractphase.isthephaseofthewavefrontsscatteredfromaesshape.

Whatinterfereheengofphaseiy，sothatphotisterpatternsinwhichthefullamplitudeaiowaveisrecorded.Theprincipleisshownihewavescatteredfromtheobjeterfereswithareferehasawell-keedbyalaser.Theiernisreadetelight-seerials:thisisthehologramitself，iedbyDenisGaborinthemiddlepartofthe20thtury.

19.Ahologramisstructedbyregtheinterfereweenareferencebeamoflightaeredfromtheobject.

&heimageisalittlemorepliwithanraph.First，areferencebeamillumihehologramaslightisscatteredfromthepatterhematerial.Thesescatteredbeamshavetheremarkablepropertythattheyreproducethebeamsscatteredfrihatasyoureyesreceivethem，itappearsthattheobjectisrestrufrontofyou.Movingaroundtheimagerevealsdiffereheobject，becausethebeamsscatteredfromthosedifferentpartsencodedifferentinformation.