应用光学教学课件 (第四章)2

Chapter4PlanesurfacesandPrismsThebehaviorofabeamoflightuponrefractionorrefractionisofbasicimportanceingeometricalopticsPlanesurfacesoftenoccurinnatureArtificialplanesurfacesareusedinopticalinstrumentstobringaboutdeviationsorlateraldisplacementsofraysaswellastobreaklightintoitscolors.Themostimportantdevicesofthistypeareprisms.2.1ParallelbeamParallelbeamremainsparallelafterreflectionorrefractionataplanesurface.Refractioncausesachangeinwidthofthebeamwhichiseasilyseentobeintheratio,whereasthereflectedbeamremainsofthesamewidth.Thereisalsochromaticdispersionoftherefractedbeambutnotofthereflectedone.cos'/cos(a)externalreflection(c)Totalreflectionatorgreatthanthecriticalangle(b)InternalreflectionatananglesmallerthanthecriticalangleReflectionatasurfacewherenincreasesiscalledexternalreflection.Itisalsofrequentlytermedrare-to-densereflectionbecausetherelativemagnitudesofncorrespondroughly(thoughnotexactly)tothoseoftheactualdensitiesofmaterials.Fig.2(b)showsacaseofinternalreflectionordense-to-rarereflection.Inthisparticularcasetherefractedbeamisnarrowbecauseisclosedto90°Externalreflectionandinternalreflection'2.2ThecriticalangleandtotalreflectionnorefractedlightCriticalangleRefractionandtotalreflection(a)Thecriticalangleisthelimitingangleofrefraction(b)totalreflectionbeyondthecriticalangleAformulaforcalculatingthecriticalanglesisobtainedbysubstituting,orinSnell’slawInthelimitingcase,wheretheincidentraysapproachanangleof90°withthenormal,therefractedraysapproachafixedanglebeyondwhichnoreflectedlightispossible.Thisparticularangle,forwhich,iscalledthecriticalangle.cc90sin190cnnsin'1Sothat'sinnncAlwayslessthanunity接近，逼近Thecriticalanglefortheboundaryseparatingtwoopticalmediaisdefinedasthesmallestangleofincident,inthemediumofgreaterindex,forwhichlightistotallyreflected.TotallyreflectionisreallytotalinthesensethatnoenergyislostuponreflectionTotalreflectionprismsTotalreflection,Porro,Doveorintverting,Amiciorroof,Triplemirror,Lummer-brodhunReflectingprismsutilizingtheprincipleoftotalreflection1.Theanglesofincidencecanbeassmallas45°.2.Therequirementsetsalowerlimitonthevalueoftheindexnofprism.45sin1'nnnIndexofair21.414nLowrefractiveindicesofopticalmaterialsLucite(n=1.49)Fusedquartz(n=1.46)一种有机玻璃材料，树脂熔石英Refractometers（折射计）InstrumentsforthedeterminationofrefractiveindexRefractionbytheprisminaPulfrichrefractometer2.3Plane-parallelplateRefractionbyaplane–parallelplateItemergesparalleltoitsoriginaldirectionbutwithalateraldisplacementdwhichincreaseswiththeangleofincidence出射ThedisplacementdStartingwiththerighttriangleABE,wecanwrite)'sin(ldBythetrigonometricrelationforthesineofthedifferencebetweentwoangles)cos'sin'cos(sinld)'coscos'sin'cos'cossin(td'costl直角三角形位移三角法的FromSnell’slaw,weobtainsin''sinnnThereforecossin(1)'cos'ndtnFrom0°uptoappreciablylargeangles,disnearlyproportionalto2.4RefractionbyaprismThedeviationproducedbythefirstsurfaceisnotannulledbythesecondbutisfurtherincreased.Thechromaticdispersionisalsoincreased,andthisisusuallythemainfunctionofaprism.Thereflectionatthesecondsurface,aswellasatthefirstsurface2211'sinsin''sinsinnnThetotalangleofdeviation11221212''('')As11'22'12''or212.5Minimumdeviation21Iftheprismisrotatedcontinuouslyinonedirectionaboveanaxisparalleltotherefractingedge,theangleofdeviationwillbeobservedtodecrease,reachaminimum,andthenincreaseagain.Thesmallestdeviationangle,calledtheangleofminimumdeviation,occursatanparticularangleofincidencewheretherefractedrayinsidetheprismmakesequalangleswiththetwoprismfaces.m1212''Howtoprovetheanglesbeequal?ThemeasurementsoftherefractiveindexInthetriangleABC,;ForthetriangleABN’,Consequentlym12''1112',2,'m1111',()22mSincebySnell’slaw21sin)(21sin'mnnPlacethesampleintheformofaprismonthetableofaspectrometerandmeasuringtheanglesand.Theformerforeachcolordesired.Whenprismsareusedinspectroscopes(分光镜）andspectrographs（摄谱仪）,theyarealwayssetasnearlyaspossibleatminimumdeviation.m2.6ThinprismsWhentherefractinganglebecomessmallenoughtoensurethat,sinmmnn21sin)(21sin'Thinprisminair)1'(nThepowerofaprismItiscustomarytomeasurethepowerofaprismbythedeflectionoftherayincentimetersatadistanceof1m,inwhichcasetheunitofpoweriscalledtheprismdiopter(D)棱镜折光度棱镜的折光本领thepoweroftheprismindioptere.g.Forthedenseflintglass,.Therefractingangleof1-Dprismshouldbe85459.067050.057300.0'1.67050Dn2.7CombinationsofthinprismsTheRisleyorHerschelprismacombinationoftwothinprismsofequalpowerwhichcanberotatedinoppositedirctionsintheirplane.ThedeviceisequivalenttoasingleprismofvariablepowerWhentheprismsareparallel,thepoweristwicethatofeitherone;Whentheyareopposed,thepoweriszero.Theresultantdeviationcos2212221cossintan212Sincealmostalways122cos22cos4)cos1(2222iiiand2tancos1sintan22.8ReflectionofdivergentraysWhenadivergentpenciloflightisreflectedataplanesurface,itremaindivergent.'ssObjectdistance