球面系统厚透镜与薄透镜

ChapterⅢsphericalsystemythinlensesandthicklenses球面系统厚透镜与薄透镜§3.1Focalpointandfocallength焦点与焦距§3.2Lensformulaforthinlens薄透镜公式§3.3Thicklens厚透镜§3.4Sphericalmirror球面反射镜SeveralstandardformsoflensPositive:thickeratthecenterEqui-convexplane-convexpositivemeniscusNegative:thinneratthecenterEqui-concaveplane-concavenegativemeniscus§3.1FocalpointandfocallengthrealfocusDivergingraysfromFarerefractedintoabeamparalleltoaxis.virtualfocusConvergingraystowardF.Parallelincidentbeamisrefracted,convergeintoF’.DivergeasifitcomefromF’FocalpointandfocallengthF:primaryfocalpointf:primaryfocallengthF’:secondaryfocalpointf’:secondaryfocallength1、Imageformationrealimageandvirtualimage＊GraphicalconstructionSharplyrealimagecanbeformedonthescreen.Virtualimagecanbeseenbyhuman,butitcannotberecorded.Becauserefractedraysdonotcomefrom''BA,onlyappeartodoso.2、ConjugatepointsandplanesPrincipleofthereversibilityoflightraysif''BAwereanobject,animagewouldbeformedatAB.TheobjectandimageareinterchangeableorconjugateA'A(B'B):arecalledconjugatepoints.Theplanethroughthesepointsperpendiculartotheaxisarecalledconjugateplane.3、Calculationmethodfrom2.1:rnnlnln'''Gaussianformulaforasinglesphericalsurface)'(ll:object(image)distanceIfl''flrnnfn''''lflrnnfn'fnfn''ornnff''fnfnlnln''''4、GraphicalconstructionsTheparallel–raymethod①TheraysfromobjectpointBtravelingparalleltoopticalaxiswillberefractedtopassthroughF’.②TheraysBCpassthroughthecenterofcurvatureisun-deviated,becauseitisinlineandCisnodalpoint.③ThetworaysaresufficienttolocatethetipoftheimageatB’.④TherayswhichpassthroughFwillberefractedparalleltotheopticalaxis.5、Oblique-raymethodsMethods1:AM:representanyrayincidentonthesurface.①ThroughthecenterofC,Adashedlineisdraw,paralleltoAM,CrossesthesecondaryfocalplaneatN,②ThelineMNisrefractedray,itcrossestheaxisofA’.Methods2:Fromsimilartriangles(p53)6、MagnificationofsphericalsurfaceLateralmagnification:theratiobetweentransversedimensionofthefinalimageandthecorrespondingdimensionoftheoriginalobject.klklklklyy'''＊ifispositive,imageiserectandvirtual＊ifisnegative,imageisinverted(inverse)andreal.7、Reducedconvergence＊Reciprocalsl1,'1l,r1,'1f,f1Actuallyrepresentcurvature,l,'l...areradii''''fnlnlnVV',V,V’arecalledreducedconvergence.Becausetheyaredirectmeasuresofdivergenceeconvergencofimageobjectwavefronts.:definetherefractingpower.＊＊Alldistancesaremeasuredinmeters,thereducedV,V’,Pareinunitscalleddiopter.Definition:whosethicknessisconsideredsmallincomparisonwiththedistancessuchasl,'l,r,'f.§3.2Lensformulaforthinlens1、FocalpointFF’(justlikesurface)＊PrimaryfocalpointFisanaxialpointthatanyraycomingfromitorproceedingtowardittravelsparalleltotheaxisafterrefraction.＊SecondaryfocalpointF’:thatanyincidentraytravelingparalleltotheaxiswillproceedtoward(orappeartocomefrom)F’afterrefraction.＊Forlenswiththesamemediumonbothsides,wehaveff'2、Derivationofthelensformula＊imageformula:'''fylyy(1)fylyyfylyy''''(2)(1)-(2)'''''''fyyfyfylyylyyyieldthedesiredformula'11'1fllGaussianform'''fxxfyy''ffxxNewtonianform＊Lateralmagnification:Frompicture:xffxyyM'''Newton(1)÷(2):llyyM''Gauss＊Opticalpower:)('1''mffn＊LensMaker’sformula:Ifalensistogroundtosomespecificf,theradiiofcurvaturemustbesochosentosatisfytheequation.)11)(1('121rrnf3、＊ThinlenscombinationFirstapplythegraphicalmethodtofindtheimagedistance,thenshownhowtocalculateitbylensformula.△Graphicalmethod:△Calculationmethod:Forlens2:'12'121'12nnyydlLApplyllyyfll'''11'14、＊Derivationoflensmaker’sformula'1'111'111'1'1fnrnnlnln(1)2'222'222'2'2fnrnnlnln(2)Forthinlens2'1llnnn2'1Add(1)+(2)11'122'211'2'2rnnrnnlnln①for21nn''212'21111'2'2fnfnrnnrnnlnln②for水nnn21f'1r1r1)(1'121）（水nnllinwater③for121nn'1)11)(1(1'121frrnllinair＊ThinlensincontactParallelraysarerefractedbyfirstlenstowarditssecondary'1F,secondlensbringstheraystogetherat'F,forsecondlens'1fistheobjectdistance,'fisimagedistance.'11'1fllForlens2'11'12'1fff'11'12'1fff21Thepowerofcombinationisequaltothesumofthepowerofindividuallens.§3.3Thicklens1、Conjugaterelationforthicklens＊RelationbetweenobjectandimageGaussianlensformula:''211''2fnfnlnlnWhen'21nn'11'1fll＊Powerformulas21'121nd111'1'1'111rnrnnfn222'2'2'221rnrnnfnThicklens:21221)1()11)(1(rnrndrrnIfd=0(thinlens),))(1(21nConclusion:＊Withlenscombinationasathinklens,thepositionofthecardinalpointsofacombinationoftwothinlensesinaircanbecalculatedbymeansofthethicklensformulas.＊ThicklensTheformula21'121ndcanbeusedindoubleseparatedlensiftake1'1n.2、Specialthicklenses＊apositivelenswithequalradiiofcurvature＊anegativelenswithconcentricsurfaceAlenswithequalradiisurroundedbyamediumoflowerindexhasasmallbutpositivepower.ThespacingHH’isequaltothelensthicknessd.Concentriclens(bothsurfaceshavethesamecenterofcurvature),ifnnn1'2,thelenshasanegativepowerwithlongfocallength.HH’=dlocatedsomedistancefromandtotherightthelens.HH’=0principalpointcoincidewiththecommoncenter.§3.4Sph