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1、应用光学应用光学44-47nThesekindsofopticalelementsarecalledprisms.Theprisminfig.4.9iscalledPentaprism(五角棱镜五角棱镜) FFIncidentfaceIncidentfaceEmergingfaceEmergingfaceConclusionEquivalentactionofaprisminopticalsystemcorrespondswithaparellelglassboard（平行平板）（平行平板）unfoldingofprismnThismethod,unfoldingtheprism,cancel
2、ingthereflectionandreplacingprismsrefractionsbyglassblocksrefraction,iscalledprismunfolding.n把棱镜的光轴截面沿着它的把棱镜的光轴截面沿着它的反射面展开反射面展开，取消棱镜的反射，以平行玻璃板的折射代取消棱镜的反射，以平行玻璃板的折射代替棱镜折射的方法称为替棱镜折射的方法称为“棱镜的展开棱镜的展开”。Theprismmustbedemandedtomeettworequirements:nAfterunfoldingtheprism,thetwofacesoftheglassblockmustbepar
3、alleltoeachother.(棱镜展开后玻璃板的两个表面棱镜展开后玻璃板的两个表面必须平行必须平行)nWhentheprismlocatesinconvergingrays,theaxismustbeperpendiculartobothincidentandemergentfaces.(如果棱镜位于会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聚光束中，则光轴必须和棱镜的入射及出射表面相相垂直垂直）Methodsofunfolding:按入射光线的顺序，以反射面为镜面，求按入射光线的顺序，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其对称像，并依次画出反射棱镜的展
4、开图。简单说：逐个作出棱镜经反射面所成的像简单说：逐个作出棱镜经反射面所成的像ABCOSSCExample 1CABBASSSExample 2Some tipical prisms4.4.1Right-angleprismACBAO1O2O3Theright-angleprismcandeviatetheaxisthroughanyangleFig.4.190-/290-/2deviatedtheaxisthroughFig.4.2Isoscelesprism4.4.2Pentaprism(五角棱镜五角棱镜)ABCDEL: the length of the axis光轴长度光轴长度D:Th
5、emaximumaperture通光口径通光口径904.5roofsurfacesandroofprisms(屋脊面和屋脊棱镜屋脊面和屋脊棱镜)Right-angleprismRoofprism两个互相垂直两个互相垂直的反射面称为的反射面称为屋脊面屋脊面nInordertogetanimagesimilartotheobject,twosurfacesat90whoseintersectionliesinthehypotenuse(斜边斜边) canbeusedtoreplaceoneofthereflectingsurfaces.nThesespecialsurfacesarecalledr
6、oofsurfaces(屋脊面屋脊面).nAprismcontainingroofsurfacesiscalledroofprism(屋脊棱镜屋脊棱镜).Whatistheroleoftheroofprism?nTheadditionoftherooftotheprismistointroduceanextrainversiontotheimageorchangethetotalreflectingnumberfromoddtoeven,keeptheoriginalaxisandimageorientationinthemainsectionunchanged.Inthiswaywecana
7、ddareflectionandgetanimagesimilartotheobject.n在不改变光轴方向和主截面内成像方向的条件下，在不改变光轴方向和主截面内成像方向的条件下，使像倒置使像倒置一次一次，或使系统总的反射次数由，或使系统总的反射次数由奇数变奇数变成偶数成偶数，从而达到物像相似的要求，从而达到物像相似的要求Fig.4.18Principleofroofsurfacex xy yz zx x y y z z x xy yz zPlanardonationmethodofroomprism屋脊棱镜的平面表示方法屋脊棱镜的平面表示方法4.6imagingpropertyofparal
8、lelglassblockandprismsizecalculationnWementionedintheprevioussectionthatbyusingaprismtoreplacemirrorscorrespondstoaddaparallelglassblock.Fig.4.21ParallelglassblockThatmeansaparallelglassblockonlymakestheimageplaneshiftacertaindistance,havingnoinfluenceontheimagingproperty.Theequivalentairthickness:(
9、4.2)n光线移动的距离随入射光线移动的距离随入射角的不同而不同角的不同而不同 n同样也随平板的厚度不同样也随平板的厚度不同而变化同而变化n上式表明上式表明:L L因不同的因不同的I I1 1值不同而不同值不同而不同. . n即从具有不同入射角的各条光线经平行平面板折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，射后，具有不同的轴向位移量，n这就说明，同心光束经平行平面板后变为非同心这就说明，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。光束，成像是不完善的。 n也可以看出平行平面板的厚度也可以看出平行平面板的厚度d d 愈大，成像不完愈大，成像不完善程度也愈大
10、。善程度也愈大。4-7determinationofimageorientationsformirrorsandprismsyzxxzyFig.4.25（a）4.7.1mirrorandprismsystemwithsinglemainsectionnmirrorandprismsystemwithsinglemainsectionmeansthatallofthemainsectionsofthemirrorsandprismscoincidewithoneanother.nIfthereisnoroofsurfaceinthesystemtheorientationofzwhichisno
11、rmaltothemainsectionwillbeparalleltoallofthereflectingsurfaces.nAccordingtothemirrorimagingproperties,theobjectandtheimagearesymmetricaltothemirror,sotheorientationofzinimagespacewillbeasthesameasthatofzintheobjectspacenomatterhowmanyreflectionshavehappened.nHowever,ifthereisaroofsurfaceinthesystem,
12、accordingtotheroofsurfaceproperty,theorientationszandzwillbereversed.nInthiswaywecaneasilydeterminetheorientationofzinamirrorandprismsystemwiththesinglemainsection.nFirstofall,supposethereisnoroofsurfacesinthesystemandmeanszwillbethesameorientationasz.nonthiscondition,ifthetotalnumberofthereflectors
13、iseven,theimagewillbesimilartotheobject,yandyhavethesameorientationiftheorientationofaxisxcoincideswithx,asshowninfig.4.25(a).nOnthecontrary,iftheorientationofaxisxisreversedtox,ywillbeoppositetoy,asshowninfig.4.25(b).nSimilarly,ifthetotalnumberofthereflectorsisodd,theimagewillbeamirrorimage,yandyha
14、vetheoppositeorientationofaxisxcoincideswithx,asshowninfig.4.26(a).nOnthecontrary,iftheorientationoftheaxisxisreversedtox,ywillhavethesameorientationasy,asshowninfig.4.26(b).nThus,foramirrorandprismsystemwithsinglemainsectionwecangetthefollowingrules,asshownintable4.2.Table4.2orientationrulesforyThe
15、emergentaxisandincident(x,x)NumberofreflectorsyandyCoincideEvenThesameorientationCoincideOddReverseReverseEvenReverseReverseOddThesameorientation总结判断单一主截面的平面镜棱镜系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：统中，主截面内成像的方向规则如下：1.1.光轴同向：光轴同向：光轴反射次数为偶数，光轴反射次数为偶数，y y和和yy同向；同向；光轴反射次数为奇数时，光轴反射次数为奇数时，y y和和yy反向。反向。2.2.光轴反
16、向：光轴反向：光轴反射次数为偶数，光轴反射次数为偶数，y y和和yy反向；反向；光轴反射次数为奇时，光轴反射次数为奇时，y y和和yy同向；同向；注意：注意：n1 1、上面提到的光轴，同向和反向是广义的，、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，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凡是光轴偏转角小于9090均认为是同向的，均认为是同向的，大于大于9090认为是反向的；认为是反向的；n2 2、当系统中有屋脊棱镜时，不影响主截面、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，计算内像方向，光轴看成是在棱上反射，计算光轴反射时只计
17、算一次，计算总反射次数光轴反射时只计算一次，计算总反射次数时，屋脊面计算两次时，屋脊面计算两次. .nIfthereisaroofsurfaceinthesystem,accordingtoitsimagingproperty,itdoesnotaffecttheorientationswhichlieinthemansection,thus,onthisconditiontheaboverulescanalsobeused.nFortheroofsurfacetheaxiscanbetakenasifitisreflectedattherooflineandthereflectornumbe
18、rshouldbecountedasontime.However,forthetotalnumberofreflectors,theroofsurfaceshouldbecountedtwice.方法方法1.x,x与光轴与光轴同向同向。2.没有没有或或偶数偶数屋脊面时，屋脊面时，z与与z同向同向；奇数奇数屋屋脊面时，脊面时，z与与z反向反向。3.当当x与与x同向同向时，时，偶次反射偶次反射y与与y同向同向，奇次奇次反射反射y与与y反向；反向；x与与x反向反向时，时，偶次反射偶次反射y与与y反向反向，奇次反射奇次反射y与与y同向。同向。ExampleA:FIG.4.27(a)、（、（b）yzxy
19、zxyzxyzx8,Similariamge7,mirroriamgeFig. 4.274.7.2 Mirror and prism system with two 4.7.2 Mirror and prism system with two main sections perpendicular to each thermain sections perpendicular to each ther123o1o2o3o4yxzyzx132Similar imageFig. 4.28123o1o2o3o4yxzyzx132o1o2o3o4Forprism1and3:Theaxisrotates
20、180,soxandxisreversed，Themumberofreflectoris2,yandyisreversed.Forprism2：Theorientationofxisoppositetoxandthemumberofreflectoris2，sozisoppositetozPrism can change the orientation of object and image in main section棱镜只能改变主截面内的物像方向棱镜只能改变主截面内的物像方向Someexamples:y yz zx xx xz zy yRight -handRight -handLeft-handLeft-handy yz zx xx xy yz zRight -handRight -handRight -handRight -handx xy yz zx xz zy y45Right -handRight -handLeft-handLeft-handyzxyzxyzxyzx结束语结束语谢谢大家聆听！谢谢大家聆听！53
