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Chapter 3 Waves（第1页）

Chapter3Waves

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。

Hologramsputergeedaalsorothermaterials。Theideaisthatthesurfaceshapemimiterferehereferendobjectwaves，sothatraisedpartsdthtfringesandlowpartstain，illuminatingthiswithareferencewavecausesscatteredlighttoimitatethewavefrontsoftheobject。Thiskindofhologramisusedasasecuritydeviebanknotes（suchastheUK￡20note，ofholographicimagesofthe18thturyScottisheSmithoheyarehardtomakeandrequireadvaneeringtocopy。