应用光学4.1-4.3

Chapter4MirrorandPrismSystemsOpticalsystemscanbeclassifiedintotwotypes:1.symmetrical(对称的),andsphericalsystems2.mirrorandprismsystemsInthepreviouschapterswehavediscussedtheimagingpropertiesoftheaxiallysymmetricalandsphericalsystems,inthischapterwearegoingtodiscussthemirrorandprismsystems.Anaxially(共轴的)symmetricalsphericalsystemhasmanyadvantagessinceitcontainsasymmetricalaxis（对称轴）.Ontheotherhand,ithassomedisadvantages:thesystemcannotturnbackorreflexsincealloftheopticalelementslocateonacommonline.Thereforethelengthordimension(尺寸)andtheweightofthesystemarecomparativelylarge.Inordertoovercomethedisadvantagesandreserve（保持）theadvantageswecancombinetheaxiallysymmetricalsystemsandthemirrorandprismsystems.Questions：Whycanaddingamirrorandprismsystemintoaaxiallysymmetricalsystemovercomethedisadvantages?Whataretheimagingpropertiesofthemirrorandprismsystems?Howtocombinethemtogether?Howtodesignthemirrorandprismsystems?Thesearewhatwewilldiscussinthischapter.4.1ApplicationsofMirrorandPrismSystemsinOpticalInstrumentsWecanmakeupvarioussphericalaxiallysymmetricalsystemsbyusinglensestomeetdifferentimagingrequirements.Forexample,atelescopeoramicroscopeisusuallycomposedofseverallenses.However,theobviousdisadvantageofaxiallysymmetricalsystemisthatthesphericalsurface’scenterofthistypeofsystemmustbelocatedatonecommonline,andusuallythiscannotmeetmanyactualapplications.Forinstance,asimpletelescopemaybecomposedofapositiveobjectiveandapositiveeyepieceandthiswillbringaninvertedimagewhichisveryinconvenientforobservation.Onthisconditionanuprightlensgroupcanbeaddedintothesystemtogetanerectedimage,asshowninFig.4.1(a).positiveobjectivepositiveeyepieceKepleriantelescopeThedimensionandweightofthistypeofsystemarecomparativelylargeandmaynotmeettherequirementsoftheopticalinstrumentsusedinmilitary,forexampleshowninFig.4.1(b),containprisms,thuscangetanerected（正立的）imagewithoutaddinganuprightlensgroup,andgreatlydiminish(减小)thedimensionandtheweightoftheinstrument.Besides,inmanyinstrumentsthelocationandthedirectionoftheaxisusuallyneedtobechangedaccordingtoactualuse,forexample,inatrenchmortar（迫击炮)theaxisofthecollimator(瞄准仪)mayneedtotilt（倾斜）anangleinactualuse,asshowninFig.4.2.Sometimes,theobserverdoesnotneedtochangehislocationanddirectionwhenobservingenemy’ssituation,andjustneedstorotatetheprismsormirrors,asshowninFig.4.3.Fig.4.3Periscope潜望镜Generallyspeaking,theusagesofprismsandmirrorsareasfollows:1）Theycanbeusedtodiminishthedimensionandtheweightofaninstrument.2）Theycanbeusedtochangethedirectionoftheimage,ortomaketheimageinverted.3）Theycanbeusedtochangethelocationandthedirectionoftheaxis,producingacertainperiscope(潜望镜)heightortiltingtheaxisforanangle.4）Withthehelpofrotatingtheprismandmirror,thedirectionoftheaxiscanbechangedcontinuously,enlargingtheobservingfieldofview4.2imagingpropertiesofmirrorsAPOQBA’Fig.4.4VirtualimageformedbymirrorNO’II’B’4.2.1theimagingpropertiesofsinglemirrorAA’NBB’OO’II’DFig.4.4Accordingtoreflectionlaw,thereflectionangleisequaltothatofincidence:∠BON=∠AON=I∠AOD=∠A’ODAD=A’DConclusion:aplanemirrorcanimageanyobjectpointsideallyinthewholespace.Propertie1.Theimageandobjectpointsaresymmetricaltothemirror.像与物相对于平面镜来讲是对称的。llrnnlnln＝，rnnPropertie2.Theheightoftheimageisequaltothatoftheobject物像大小一致，且成正象。lnlnllnn1中指代表Z轴PQxyzy'x'z'OO’大拇指代表X轴食指代表Y轴Theimageorientationofamirror:righthandcoordinatesinobjectspaceRighthandLefthandRighthandLefthandMirrorimage,RighthandRighthandSimilarimage,Odd(奇)mirrorsEven奇次镜面反射成镜像；偶次镜面反射成相同的像。镜像与一致像1）所谓镜像是指若物为右手坐标，像为左手坐标，这种像叫为镜像。特点：像物同向，左右颠倒(方向相反)，可通过奇次反射得到。2）一致像：物为右手坐标，像也为右手坐标，即物与像是完全一致的，它可通过偶次反射来得到。＊Asingleplanemirrorhasthefollowingproperties:Aplanemirrorcanformanidealimageinthewholespace,andtheimageandobjectpointsaresymmetricaltothemirror.Theheightoftheimageisequaltothatoftheobjectbutdifferentinorientation.PPP1O1A2''O2qAA’1A2βαγγ-αβγ-α4.2.2theimagingpropertiesoftwomirrorsq22AAPq4.3rotationofmirrors∠A’OA”=2∠POP’4.3.1rotationofasinglemirrorConclusion:Ifamirrorrotatesanangleofαroundanaxisperpendicular(垂直)toincidentplane,theincidentanglechangesα,andtheangleofreflectedrayswillchange2α.Therotationdirectionoftherayisthesameasthatofthemirror.-fApplicationofopticalcomparator(比较仪)MAA'MHH'L1PPa支点测杆a)graticule分划板MirrorLensfixedPivot支点Pole测杆PP测杆aMA'AML1HH'F'-fb)Pole测杆axtgxfAAtg2△x:movingamount4.3.2TranslationeffectofasiglemirrorQPA’ABA”h2hQ’P’B’P’A′A″=2hO2O1qqPPPAMNI1I1I2I2β≤90q212122IIIIq24.3.3PropertiesoftwomirrorsConclusion:Foranyincidentraythatliesinaplane(主截面)perpendiculartothetwomirrors,therotatedangleoftheemergenceraywillbeequaltotwicetheangleofthetwomirrors,regardlessoftheincidentray’sdirection。TherotationdirectionwillcoincidewiththatofrotationfromP1toP2accordingtotheorderofreflectionsonthetwomirrors.4.3.4RotationeffectoftwomirrorsConclusion:Aslongastheangleoftwomirrorskeepsunchangedthedirectionoftheemergingraywillnotchangedevenifthepositionofthetwomirrorshavesomeshift.Butthepositionoftheemergingrayhassomeparelleldisplacemen