大学物理Chap31-OpticDif

Chapter31DiffractionandPolarization1.DiffractionofLight2.DiffractionGratings3.X-RayDiffraction4.PolarizedLightWhentheslipwider,lighttravelsinstraightline.31-1.DiffractionofLight(P703)1.Diffraction(衍射)byasingleslitscreenshadowscreenWhentheslipgetsnarrow,thelightproduceadiffractionpatternonthescreen.Whenmonochromatic(单色)lightfromadistantsourcepassesthroughanarrowslitorobstacle——producesadiffractionpattern(光能绕过障碍物的边缘传播形成具有明暗相间的衍射图样)iscalleddiffractionoflight(P703).Conditionofdiffraction:thewidthofslit(dimensionofbarrier)issimilartothewavelengtha～λ波传到的任何一点都是子波的波源，各次级子波在空间某点的相干叠加，就决定了该点波的强度。Hugens-Fresnel’sprincipleRecalling:Themethoddiscussinglocationofdiffractionpatternforasingle-slitdiffractioniscalledfresnel’half-wave-zonemethod(半波带).2.Locatingthediffractionbands(P704)*SffaLL·ABslitaEOδPsinmaxaPathdifferenceofA→P&B→P:screenLensdoesn’tproduceadditionallight-pathdifference.Twohalf-wave-zonescanbegotten,andPisfirstdarkfringe(outofphasepairsrays)Inasingle-slitdiffractionexperiment,darkfringesareproducedwherethepathlengthdifferences(asin)betweenthetopandbottomraysareequaltol,2l,3l,.centralbright(中央明纹)firstdarkfringesinmaxa(ii)lsina(i)00，firstbrightfringeaP屏幕screenl23sina(iii)Conclusion:0sinaoppositetotheconditionofinterferencepatternllsini.e.abright,3,2,12)12(dark,3,2,1sinmmmmallAngular-width(角宽度):al2210tansinForcentralbrightfringe:Linear-width:affxl2ant210whena0x1:半角宽度021xafxl——halfofthecentralwidth.其他明纹宽度为中央明纹宽度的一半tansinaaFor1-orderdarkfringe,lfxa1afxl1Similarly,for2-orderdarkfringe,afxl22Positionof1thdarkfringe一级暗纹坐标Positionof2thdarkfringeWidthofeachorderofbrightfringes:Solution:Aslit1.00mmwideisilluminatedbylightofl=589nm.Weseeadiffractionpatternonascreen3.00maway.Whatisthedistancebetweenthefirsttwodiffractionminimaonthesamesideofcentraldiffractionmaximum?lmasin11tanfx22tanfxmm77.1)2(12aafxxxllTheseparationofthetwominimais:Usingtheconditionofminimaofdiffraction:andExample:3.Intensityinsingle-slitdiffraction(P705)(a)Thecentralmaximum;(b)Betweencenterandfirstminimum;(c)Thefirstminimum;(d)Nearsecondarymaximum.SeeFig.31-8inP706)sin(π2lx当增加,半波带数增加,未被抵消的半波带面积减少,所以光强I变小.i.e.,I31-2.DiffractionbyaCircularApertureDiffractionpatternofacircularaperture(P710):BasicarrangementofexperimentS*dlL1fBasedontheoreticalcalculation,thefirstminimumofdiffractionpatternofacircularapertureofdiameterd(radiusr)locates(第一级暗环的衍射角满足):rdll61.022.1sin1drll22.161.0sin11Angular-radiusofcentralmaximum(艾里斑):Ifdl,diffractioncan’tbeseen仅当通光孔径足够大时,艾里斑才可能很小.占入射光总光强的84%dlAiryspotgettingsmallTheangularseparationofthetwopointsourcesissuchthatthecentralmaximumofthediffractionpatternofonesourceiscenteredonthefirstminimumofthediffractionpatternoftheotheraconditioncalledRayleigh’scriterionforresolvability.瑞利判据：如果一个点光源的衍射图像的中央最亮处刚好与另一个点光源的衍射图像第一个最暗处相重合,认为这两个点光源恰好能为这一光学仪器所分辨。Resolvability(分辨)&Rayleigh’scriterion(判据)(P710):Itcanbeseenfromthetextgiveninpage710thatdlIncreasingRTheconditionoftwoobjectsarebarelyresolvedbythiscriterionofanangleseparationR(最小分辨角):dRl22.1arcsinForsmallangle,dRl22.1(Rayleigh’scriterion)l22.11dRRResolvability(分辨本领):s1d**s2RRhxRRdl22.1rad10310160105732m2Itissaidthatacamerainaspy-satellitecandistinguishclearlythenumberofcar’slicenceruuningontheroad.Solution:AnangleseparationRTodistinguish(要识别)thedistanceof5cmbetweennumbersonalicencefromtheheightof160km,whatshouldthecircularapertureofdiameterdbe?(Assumel=500nm).Example:31-3.Diffractionbyadoubleslit(P708)Nodiffraction:λθadfLensIθθConsideringthediffractionoflight.设双缝缝宽均为a，在夫琅禾费衍射下，每缝衍射图样位置相重叠differenceofinterference&diffractionThinkof:II00d23ld2ld2ldld23ldlTheplotofFig.31-10csuggeststheinterferencepatternfortwoactualslits.ThatplotwasconstructedbyusingthecurveofFig.31-10basanenvelopeontheintensityplotinFig.31-10a.Thepositionsofthefringesarenotchanged;onlytheintensitiesareaffected.31-4.DiffractionGratings(衍射光栅)(P713)Oneofthemostusefultoolsinthestudyoflightandofobjectsthatemitandabsorblightisthediffractiongrating.abPO1.Characteristicparameters(1)Thewidthofaslit:a(2)Separationbetweenslits:dItisalsocalledgratingspacing光栅常数:d=a+b(10-4~10-6m)2.ThediffractionpatternofgratingsDiffraction-patternofgratingsisthesuperpositionofsingle-slitdiffractionandN-slitinterference.IfNrulingsoccupyatotalwidthw,thend=w/N(3)Forgrating,theslitsonitareoftencalledrulings(划线)orlines.光栅公式(i)Ifthepathlengthdifferencebetweenadjacentraysisanintegernumberofwavelengths,i.e.lmdbasinsin)((m=0,1,2,…)—principalmaximaTheimportantdifferencebetweenadouble-slitandmultiple-slitdiffractionpatternisthatbrightmaximaaremuchsharper&narrowerforgrating.two-slitsix-slitP714(ii)Missingorderwillbeemerged,ifdsin=mlanddmammadmi.e.,3,2,1masin=±m'lCentralbrightfringeswillvanishwhichordersaccordwithd/abeingintegernumber(级次为d/a的整数倍的那些主极大消失).Thereare500rulingsin1cmonagrating,thewavelengthl=589.3nm.Howmanyfringescanbeseeniflightperpendicularlyincident?From(a+b)sin=mland||90ºlsinbamlba