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Chapter 2 Light rays（第1页）

Chapter2Lightrays

Takingaselfierequiresthatthephonecameraispoiowardsyou。It’sobviousthatthisisnecessaryifyouaretobeiure。Butthissimplefadiethingaboutthe:toseeanimageofaherehasthtliheobjethiscaseyou）andthes。Thisisusuallycalledthe‘li’。Thuslightissomethingthatpropagatesinastraightliheobjecttotheviewer。Ihisiswhatwemightexpeeoftypesoflightsource。Eye-gvisualefecertsaregeedusinglasers，illumiageandtheperformerswithchtbeams。Laserpointersareoalksorlephasizeimagesorwordsohebeamproducedbythesetlightsourcesishighlyfocused，hardlydivergingatallevenacrossabighall。Itgoesinastraightline-youpoihedirewhereyouwaogo，anditdoesso。

Belightdoesnotobviouslyexhibitthischaracteristic，itrequiredsomethinkihatthepropagationoflightinastraightlilywhatwasouandwhydistasappearedtobesmallerthannearerowasknownthattheywere，ihesamesizephysically。

5。Eustruofraysshowingwhyobjeesizelooksmallerwhehera>

&thattheceptht-liiohisefectisattributedtoEuclid，wreearound300bce。Hisidea，fromobooksonoptics，isillustratedinFigure5。Imagiwoli’scallthemrays-ohetopoftheobject（apillarinthiscase）totheobserver’seye，aiomoftheobjecttotheeye。Theaheseisrelatedtotheappareheimageofthisobjectthatweperceive。Amoredistantpillar，thesamephysicalsizeasthefirst，producestworayswhoseaerseattheobserverissmaller-hehepillarappearssmaller。Thisisetheimage。

Whatisthestufthattraversestherays?Euclid（buildingonearlierideas）thoughtthatitartitoutfromtheeyeitself（fromanimaginaryinterillumiaedbacktotheobserver。Butthissuggeststhatwewouldbeabletoseethiitwasdarkoutside。heideaofstufmovingaloweeandobserverremainedapowerfulcept。

ItwasmodifiedbyAl-HazehthatweisareilluminatedbyraysfromtheSuernalfire）aeredtowardstheobserver。Thereareseveralstoriesabouthowhecametothisidea-ingdoiwhelyattheSuermihepaiionheexperiencedwouldbethereallthetimeifthe‘internalfire’wereburnihus，heargued，thesourceofthelightogeheimagewasexternal。

&us，forthesakeumewhatmovesalongtheseraysareparticlesoflight:callthemphotohebeamisrelatedtothetherayinoneseordertouandhowanimageofaisformed，we’llosiderenswhehesephotoedofamirroredsurface，aswellasehiswillleadtothe‘lawsofoptics’thatareusedfningveryplexoptistrumentssuchassurgicalmicrosdcathetersfor‘keyhery，asticaltelescopesplaorbitabovetheEarthfdistaheimpactoftheseisonourlifeandoftheworldisimmense。

Whatsortofpropertiesdotheseparticlesoflightpossess?Theusualsortsofattributesassigoaparticleareitsposition，itsdireoftravel，anditsspeed。Fornow，assumethatitmovesatthe‘speedoflight’，withoutgoiailaboutwhatthatactuallyis。Thepositionofaphotonmightthehestartingpositionofthe‘ray’aioon’smotiohedireoftheray。Thephotonheadsoffromitsstartingpointinthisdireatthespeedoflightuersthesurfaceoftheobject。

&ion

&stheobject，thelightisreflected。ensisthatthephotohesurfagingitsdire，butnotitspositiononthesurface。Thesituationisshownihemannerinwhichthedireisgedisspecifiedbythe‘lawofrefle’，discoveredbyHeroofAlexandriaiury。Itstatesthattheangleofiis，theaheiningraydiredthedireperpendiculartothesurfaceatthepointofince）isequaltotheaion（thatis，theaheoutgoingraydiredthedireperpendiculartothesurfaceatthepointofiherearescesofthisceptuallysimplearemelypo>

6。Raysofa。aflatmirrorandb。andc。acurvedmirror。

ThisbeexplaiirelybyHero’slawofrefle。Figure7showsheesareflewithoppositehaheclockwise-pointingarrowistheobject。Raysfromeatonthearrowrefleirrorandarerearrathearrowseeninthemirrorispointinganticlockwise。Youusethesamestrutoshoointingarrowisseeninthemirrht-pointingarrowaanup-pointingarroointingup，andadown-pointingarrowpointsdowion。

Imagingusiio

If，insteadoflookingatyouropposite-handedselfinaflatbathroommirror，youseeyourrefleapolishedspoon，theortedforme:maguresrounds。Thetsurfaceofthespooheobjedthevexbacksurfaifiesit。

7。Thegeofhandednessofobjectsrefleamirror。

Whyisthis?Siionofimagesisperhapsthemostimportantappliofoptistruments-rangingfromtasesforvisioospacetelescopesforstificdiscovery-it’swexactlyho>

Uptonow，I‘vesideredonlyasinglerayoflightfromoo。Infact，raysusuallysalldireeachobjet。sidera‘bundle’ofsuchraysallasio，fadtheinalray。Thiseofraysdivergesasitmovesawayfromtheobject，asshowniherayshitthecurvedmirrorsurfaceatdiferentpointsandthereforealslesofiheyrefledifereions，eaestillsatisfyingHero’slawofrefle。

8。Imageformationbyaraybundleusingacurvedmirror。Theraysfromooatointheimage。

Infaagdeventuallyallmeetatasihisisthe‘image’pointi。

Animageaswenormallysideritismadeupofmultiplesuchimagepfromdiferes。Thesizeoftheimageisdetermiafromthemirrorandthefogpowerofthemirror，specifiedbytheradiusofcurvature。amoreirrorhasasmallerradiusofsurfacecurvature）。Theimagebebiggerthaheobjectisirrorthaheratioofimagetoobjectsizeiscalledthemagnifi。

Theimage-magureofacurvedmirrorwasusedbyodesignatelescope，showninFigure9。Hisdesignhasaremarkableproperty:itfesofdistaarethesamesizeforeverycolour（saidtobefreefrom‘aticaberratiooncleverlyusedthepropertythattheangleofareflectedrayforafixedaheirayisthesamehecolourofthelight。Theimageofeachcolouristhereforeformedinthesameplace-allthecisterperfectly，guaranteedbyphysics。

&telesabledimageswithoutaticaberration。

&ion

&ohisibecausethetelescopesusedbyporarypioneerssuchasGalileoGalileiandJohannesKeplersuferedseriouslyfromaticaberration。Theimagesformedbytheirtelescopesalwayshadablurredcolouredhaloarouheobject。Thereasonforthisisthattheyweredesignedusiprhtrays-refra:thephelightraysbeheygofromoramediumtoanother。

Itistherefraoflightthatproducesthe‘kink’observediiallyimmersedinabowlofwater。ThisisdescribedbythelawofrefraonlyknownasSnell’slaw，afterDutWillebrordSh-turypropohislawsaysthattheaingraymakeserpendiculartothesurfaceisrelatedtotheaheiningraybythepropertiesofthetwomediathatformtheinterfaplethesurfaceofthewater。Thisisillustratediheparticularpropertyofthemediathatisrelevahe‘refradex’。Therefradexbethoughtofasbeingameasureoftheoptiess’ofthemediumasexperiencedbyalightray。Solighttravelsmoreslowlyihalargerrefradexbecausethemoleediumareslightlymoreresistanttohaviomsarohelight。Itislikerunninginapoolofwater。Ifthedepthisverysmall，ysmoveeasilyandyoufast。Ifthetoyourk’sharder，becauseyouhavetaiaer。Infact，thelawofrefrabederivedfromthisanalogy。PierredeFermatshowedthatwhenlightgoesfromapoioapointinaseeksaraythattraversesashortertimeihhighrefradexaimeihalowerrefradex。Thisrequiresthelightraytobendatthisiweewomedia，a’spriurnsouttobeehesameasSnell’slaw。

10。Refraofarayattheiweenairand>

Imagingusinglenses

Now，justasacurvedreflegsurfaageofa，soacurvedtrasurface。HoensisshowninFigure11。Abundleofraysfromapoiarebroughttofocusattheimage。hatdoesthis-ithasthesamecrossseasalentil。Thisistheinoftheword‘lens’。