应用光学4.4-4.7

Insec.4.3wehavementionedthatinordertokeeptheangleoftwomirrorsunchanged,thetwomirrorsareusuallymadeonacommonglass.4.4prism(棱镜)anditsunfolding(展开)Thesekindsofopticalelementsarecalledprisms.Theprisminfig.4.9iscalledPentaprism(五角棱镜)Fig.4.10showstheappearanceofaright-angleprism.Itisatrianglecylinder(三角柱体).Theplaneorsectionwhichisperpendiculartoeachprismiscalledmainsection(主截面).Therayslieinthemainsectionwillliestillinthesamesectionafterpassingthroughtheprism.Fig.4.10＊BasicdefinitionBACOpticalaxis:ABCLengthofABC:AB+BCGeometricallengthofaxisIncidentface：ACEmergingface：BCWorkingface：AC,BC,ABRidge楞：theintersectionlineofworkingfaceMainsection(主截面,光轴截面)：ABCfaceBACOpticalaxis：themiddlelineofworkingfacePrincipalsection：2ComplexPrism＊EquivalentactionofprismF′FPFIncidentfaceEmergingfaceFF'IncidentfaceEmergingface＊ConclusionEquivalentactionofaprisminopticalsystemcorrespondswithaparellelglassboard（平行平板）＊unfoldingofprismThismethod,unfoldingtheprism,cancelingthereflectionandreplacingprism’srefractionsbyglassblock’srefraction,iscalledprismunfolding.把棱镜的光轴截面沿着它的反射面展开，取消棱镜的反射，以平行玻璃板的折射代替棱镜折射的方法称为“棱镜的展开”。Theprismmustbedemandedtomeettworequirements:Afterunfoldingtheprism,thetwofacesoftheglassblockmustbeparalleltoeachother.(棱镜展开后玻璃板的两个表面必须平行)Whentheprismlocatesinconvergingrays,theaxismustbeperpendiculartobothincidentandemergentfaces.(如果棱镜位于会聚光束中，则光轴必须和棱镜的入射及出射表面相垂直）Methodsofunfolding:按入射光线的顺序，以反射面为镜面，求其对称像，并依次画出反射棱镜的展开图。简单说：逐个作出棱镜经反射面所成的像ABCOSS’C’Example1CABB’A’SS’S’’Example2＊Sometipicalprisms4.4.1Right-angleprismACBA’O1O2O3Theright-angleprismcandeviatetheaxisthroughanyangleFig.4.1α90°-α/2deviatedtheaxisthroughαFig.4.2Isoscelesprism4.4.2Pentaprism(五角棱镜)ABCDEDL22L:thelengthoftheaxis光轴长度D:Themaximumaperture通光口径90°4.5roofsurfacesandroofprisms(屋脊面和屋脊棱镜)Right-angleprismRoofprism两个互相垂直的反射面称为屋脊面Inordertogetanimagesimilartotheobject,twosurfacesat90°whoseintersectionliesinthehypotenuse(斜边)canbeusedtoreplaceoneofthereflectingsurfaces.Thesespecialsurfacesarecalledroofsurfaces(屋脊面).Aprismcontainingroofsurfacesiscalledroofprism(屋脊棱镜).Whatistheroleoftheroofprism?Theadditionoftherooftotheprismistointroduceanextrainversiontotheimageorchangethetotalreflectingnumberfromoddtoeven,keeptheoriginalaxisandimageorientationinthemainsectionunchanged.Inthiswaywecanaddareflectionandgetanimagesimilartotheobject.在不改变光轴方向和主截面内成像方向的条件下，使像倒置一次，或使系统总的反射次数由奇数变成偶数，从而达到物像相似的要求Fig.4.18Principleofroofsurfacexyzx′y′z′xyzPlanardonationmethodofroomprism屋脊棱镜的平面表示方法4.6imagingpropertyofparallelglassblockandprismsizecalculationWementionedintheprevioussectionthatbyusingaprismtoreplacemirrorscorrespondstoaddaparallelglassblock.Fig.4.21Parallelglassblock1Thatmeansaparallelglassblockonlymakestheimageplaneshiftacertaindistance,havingnoinfluenceontheimagingproperty.Theequivalentairthickness:nLe/(4.2)光线移动的距离随入射角的不同而不同同样也随平板的厚度不同而变化11221111sinsincos1'cos'sinIInIdIIIdZ111tgI'tgId'L上式表明:ΔL′因不同的I1值不同而不同.即从具有不同入射角的各条光线经平行平面板折射后，具有不同的轴向位移量，这就说明，同心光束经平行平面板后变为非同心光束，成像是不完善的。也可以看出平行平面板的厚度d愈大，成像不完善程度也愈大。§4-7determinationofimageorientationsformirrorsandprismsyzxx′z′y′Fig.4.25（a）4.7.1mirrorandprismsystemwithsinglemainsectionmirrorandprismsystemwithsinglemainsectionmeansthatallofthemainsectionsofthemirrorsandprismscoincidewithoneanother.Ifthereisnoroofsurfaceinthesystemtheorientationofzwhichisnormaltothemainsectionwillbeparalleltoallofthereflectingsurfaces.Accordingtothemirrorimagingproperties,theobjectandtheimagearesymmetricaltothemirror,sotheorientationofz’inimagespacewillbeasthesameasthatofzintheobjectspacenomatterhowmanyreflectionshavehappened.However,ifthereisaroofsurfaceinthesystem,accordingtotheroofsurfaceproperty,theorientationsz’andzwillbereversed.Inthiswaywecaneasilydeterminetheorientationofz’inamirrorandprismsystemwiththesinglemainsection.Firstofall,supposethereisnoroofsurfacesinthesystemandmeansz’willbethesameorientationasz.onthiscondition,ifthetotalnumberofthereflectorsiseven,theimagewillbesimilartotheobject,y’andyhavethesameorientationiftheorientationofaxisx’coincideswithx,asshowninfig.4.25(a).Onthecontrary,iftheorientationofaxisx’isreversedtox,y’willbeoppositetoy,asshowninfig.4.25(b).Similarly,ifthetotalnumberofthereflectorsisodd,theimagewillbeamirrorimage,y’andyhavetheoppositeorientationofaxisx’coincideswithx,asshowninfig.4.26(a).Onthecontrary,iftheorientationoftheaxisx’isreversedtox,y’willhavethesameorientationasy,asshowninfig.4.26(b).Thus,foramirrorandprismsystemwithsinglemainsectionwecangetthefollowingrules,asshownintable4.2.Table4.2orientationrulesfory’Theemergentaxisandincident(x,x’)Numberofreflectorsy’andyCoincideEvenThesameorientationCoincideOddReverseReverseEvenReverseReverseOddThesameorientation总结判断单一主截面的平面镜棱镜系统中，主截面内成像的方向规则如下：1.光轴同向：光轴反射次数为偶数，y和y’同向；光轴反射次数为奇数时，y和y’反向。2.光轴反向：光轴反射次数为偶数，y和y’反向；光轴反射次数为奇时，y和y’同向；注意：1、上面提到的光轴，同向和反向是广义的，同向不仅仅指入射光轴和出射光轴平行，凡是光轴偏转角小于90均认为是同向的，大于90认为是反向的；2、当系统中有屋脊棱镜时，不影响主截面内像方向，光轴看成是在棱上反射，计算光轴反射时只计算一次，计算总反射次数时，屋脊面计算两次.Ifthereisaroofsurfaceinthesystem,accordingtoitsimagingproperty,