我的哈工大考研光學(xué)

HW:8.43,8.44,8.68.25,8.28,8.29,8.32,8.33,8.34,8.38,8.39*SPDLB1.InanexperimentofFresneldiffractionbyacircularaperture(seethefigure),thedistancefromthepointsourceofλ=0.63μmtothediffractingscreenisL=1.5m,andthatfromthediffractingscreentoobservationoneD=6.0m.Whenthediameterofthecircularapertureisincreasedstartingfrom0.5mm.Pleasefind:(1)Thediametervaluesofthecircularaperturewhenthebrightspotsappearingataxispointforthefirstandsecondtimes.(2)Thediametervaluesofthecircularaperturewhenthedarkspotsappearingataxispointforthefirstandsecondtimes.

記憶2.InFresneldiffractionbyacircularaperture,whenthecircularaperturecontains1.5half-periodzones,findtheratiooftheintensityofdiffractiontothatofthefreepropagationattheaxispointP.ContentsIntroductionTheHuygens-FresnelPrincipleKirchhoff’sscalardiffractiontheoryBabinet’sPrincipleFresneldiffractionFraunhoferdiffractionChapter8DiffractionDiffractionofoceanwaterwavesOceanwavespassingthroughslitsinTelAviv,IsraelDiffractionoccursforallwaves,whateverthephenomenon.8.1IntroductionI.Whatisdiffraction?Whenlightencountersanobstacle,aregionofthewavefrontwillbealteredinamplitudeorphase.Asaresult,lightdeviatesfromtherectilinearpropagationlaw.Thephenomenonisdiffraction.8.1IntroductionThereisnosignificantphysicaldistinctionbetweeninterferenceanddiffraction.Itissomewhatcustomarytospeakofinterferencewhenconsideringthesuperpositionofonlyafewwavesanddiffractionwhentreatingalargenumberofwaves.Evenso,onereferstomultiple-beaminterferenceinonecontextanddiffractionfromgratinginanother.Howtodescribethepropagationoflight

Withthedecreaseintheaperturesize,diffractionbecomesdeterminant.Withtinyaperture,thediffractedwavelookslikesphericalwave.IIHuygens-FresnelPrincipleHuygensPrincipleIfweknowthewavefrontatt=0,Whereisthewavefrontalittlelater?HuygensPrinciple:Eachpointofthewavefrontgeneratesanew(spherical)waveThenewwavefrontistangenttoalloftheindividualwavefronts

Everyunobstructedpointofawavefront,atagiveninstantofawavefront,servesasasourceofsphericalsecondarywavelets(ofthesamefrequencyastheprimarywave).Theamplitudeoftheopticalfieldatanypointbeyondisthesuperpositionofallofthesewavelets(consideringtheiramplitudesandrelativephases)II.Huygens-FresnelPrincipleFresnel

IntegralEquation(菲涅耳積分式)

Obliquityfactor記憶

FresnelDiffractionFresnel-KirchhoffdiffractionEquation(8.4)Huygens-Fresneltheoryismerelypostulatedratherthanderivedfromfundamentalprinciples.TheKirchhoftreatmentshowthattheresultsareactuallyderivablefromthescalardifferentialwaveequation.TheFresnel-Kirchhoffdiffractionformula：：If

，So

TheBabinet’sprinciplestatesthatthewavedisturbanceEa(P)atanypointofobservationPduetoadiffractingscreenSa

addedtothedisturbanceEb(P)duetothecomplementaryscreenSb

atthesamepointPequalsthedisturbanceatPduetotheunobstructedwave.Babinet’sPrinciple=+巴俾涅原理：由一對(duì)互補(bǔ)光屏分別在某個(gè)給定場(chǎng)點(diǎn)引起的衍射光場(chǎng)復(fù)振幅之和，等于沒有光屏情況下，該場(chǎng)點(diǎn)的光振動(dòng)之復(fù)振幅。

=+巴俾涅原理complementaryscreens

Examplesofcomplementaryscreens,labeledSa

andSb已知光源發(fā)出的光波在自由空間中及透過某個(gè)光屏的復(fù)振幅分布，則兩者之差即該光波透過相應(yīng)互補(bǔ)屏的復(fù)振幅分布。在遠(yuǎn)場(chǎng)條件下，一對(duì)互補(bǔ)屏引起的衍射圖樣具有相同的形狀，只是中心點(diǎn)的強(qiáng)度大小不同而已。巴俾涅原理的意義Thediffractionpatternofaholeisthesameasthatofitsopposite!

HolesAnti-

HolesThediffractionpatternofaholeisthesameasthatofitsopposite!Neglectingthecenterpoint:Babinet’sPrinciple

Imagethatwehaveanopaqueshield,,containingasinglesmallaperturewhichisilluminatedbywaves.Theplaneofobservationisascreenparallelwith.

III.FraunhoferandFresnelDiffraction*SPDLB

FresnelDiffraction(菲涅耳衍射：近場(chǎng)衍射)

Wheniscloseto,theimageoftheapertureisclearlyrecognizabledespitesomeslightfringingarounditsperiphery.Asismovedfurtherawayfrom,theimageoftheaperture,althoughstilleasilyrecognizable,becomesincreasinglymorestructuredasthefringesbecomemoreprominent.ThephenomenonisknowasFresnelornear-fielddiffraction.

FraunhoferDiffraction

Ataverygreatdistancefrom,theprojectedpatternwillhavespreadoutconsiderable,bearinglittleornoresemblancetotheactualaperture.Thereaftermovingessentiallyonlychangesthesizeofthepatternandnotitsshape.ThephenomenonisknowasFraunhoferorfar-fielddiffraction.ConsiderapointsourceSandapointofobservationP,wherenolensesarepresent.Aslongasboththeincomingandoutgoingwavesapproachbeingplanarovertheextentofthediffractingapertures(orobstacles),Fraunhoferdiffractionobtain.WhenSorPorbotharetoonear,

Fresneldiffractionprevails.菲涅耳衍射:P衍射物光源觀察屏夫瑯禾費(fèi)衍射:P點(diǎn)在無(wú)窮遠(yuǎn)8.3FresnelDiffraction8.3.3-4CircularAperturesandObstacles(菲涅耳圓孔和圓屏衍射)CircularaperturesConsiderthatamonochromaticsphericalwaveincidentonascreenwhichhasasmallhole.Fresnel’sprocedureappliedtoapointsourcecanbeusedasasemiquantitativemethodwithwhichtostudydiffractionatacircularaperture.其基本出發(fā)點(diǎn)：次波相干疊加→矢量合成LetusnowexaminethefreepropagationofasphericalmonochromaticwaveemittedfromapointsourceS.Wedividethewavefrontintoanumberofannularregions.TheboundariesofthevariousregionscorrespondtotheintersectionsofthewavefrontwithaseriesofspherescenteredatPofradiusr0+/2,r0+,r0+3/2etc.ThesearetheFresnelorhalf-periodzones.half-periodzones(半波帶法)

half-periodzonesl=λ/2（1）Dividingthewavefrontintoanumberofannularregions(把波前分割成為一系列環(huán)形半波帶)（2）ThecomplexAmplitudeofeachhalf-periodzones

(每個(gè)半波帶的復(fù)振幅)(3)ThesumoftheopticaldisturbancefromallnzonesatP0(合振幅)：

（4）Thevalueof(比較各個(gè)振幅的大小)Where：

，Weget

dependsonthe

.Askincreases,decreasesslightly(tozero)Consideringastheareaofthehalf-periodzonesConstantFromH-FPrinciple：Thecanalsobereformulated:記憶5）求露出前n個(gè)半波帶的圓孔(CircularApertures)衍射中心場(chǎng)點(diǎn)Po處的合振幅

FresnelDiffraction---CircularAperturesn:oddn:evenForthefreepropagationofasphericalwave(自由傳播時(shí))，AbrightspotatPo，AdarkspotatPo

CircularAperturesdiffraction(圓孔衍射)withincreasingofρradiusBrightatPoDiscussion:Ifniseven,eachadjacentcontributionisnearlyequal,SoI0.

DarkatPo

IfnisoddAndalsoforbWiththeincreasingsizeofcircularapertures,thesensordetectaseriesofrelativemaximaandminima.(b)b=1.35m(c)b=1.60m(d)b=2.00m(e)b=2.70m(a)b=1.14m(f)b=4.00mb/m24681012141.00.508.3.4

CircularObstacles圓屏TheopaqueCircularObstacleobscuresthefirstnzones,thenThereisabrightspoteverywherealongthecentralaxisregardlessrandn.8.3.2Aphasormethod先以圓孔只露出(firstFresnelzone)第一個(gè)半波帶為例Ifnisnotaninteger,i.e.afractionofazoneappearsintheaperture,theirradianceatPissomewherebetweenzeroanditsmaximumvalue.Procedure(1)ThefirstFresnelzoneisdividedintomsubzonesbytheintersectionofspheres.(將半波帶分割成m個(gè)更窄的小環(huán)帶

)(2)Thecomplexamplitudeofeachsubzone(每個(gè)小環(huán)帶在P0點(diǎn)的復(fù)振幅)………(3)Thevectoradditionofthesubzonephasors(4)FromOtoitsedgeM,

thesumodtheopticaldisturbancesisThepolygonofvectors(多邊形)Ahalf-periodzonescorrespondingtoaphasedifferenceof(一個(gè)完整半波帶首尾矢量的位相差是)4)Discussion(若被分割的是整個(gè)半波帶，時(shí),矢量圖為半圓形弧線，合成矢量為半圓的直徑)Whenthenumberofsubzonesisincreasedtoinfinity(i.e.,),thepolygonofvectorsblendsintoasegmentofasmoothspiral.Forthefreepropagation,spiralsintothecenterofthefirstcircle(自由傳播時(shí)，螺旋線旋繞到圓心C。合成矢量為第一個(gè)半圓的半徑)ForeachadditionalFresnelzone,thevibrationcurveswingsthroughonehalf-turnandaphaseofitasitspiralsinwardbecauseoftheinfluenceoftheK(θ).(每個(gè)半波帶形成的合矢量（半園的半徑）逐漸收縮形成螺旋線)記憶Example：AcircularaperturecontainsahalfFresnelzone,pleasefindthediffraction

irradianceatP0光強(qiáng)為自由傳播時(shí)的兩倍此時(shí)園孔露出部分是半個(gè)半波帶

Solution:作圖過程仍然如前所述FromOtoB,thephasedifferenceis1.TheFresnelZoneplateIfweremovedallofeithertheevenoroddzones,atremendousincreaseinirradianceatPwouldbeobserved.Forexample,weconstructaplatewhichpassesonlythefirstoddzones.8.3.5TheFresnelZonePlate

(菲涅耳波帶片)Ascreenwhichaltersthelight,eitherinamplitudeorphase,comingfromeveryotherhalf-periodzoneiscalledazoneplateFresnelDiffractionTheFresnelZonePlate定義：將偶數(shù)個(gè)或奇數(shù)個(gè)半波帶遮擋住，就形成菲涅耳波帶片。Example：Acircularaperturecontains20half-periodzones,ifweconstructeditthatpassedonlytheoddzones.PleasefindtheirradianceataxispointP.波帶片的孔徑內(nèi)有20個(gè)半波帶，遮擋偶數(shù)個(gè)半波帶，求軸上場(chǎng)點(diǎn)P0處的光強(qiáng)？Similartoaconverginglens.2）CalculatingtheradiiofthezonesTheradiusofthekthFresnelzonesisgivenby記憶4）thethin-lensequation(成像公式)WehaveTheradiusofthethekthzone

Thenumberof

Fresnelhalf-periodzonesPSOMkOkRbb+kl/2rkhkTheFresnelZoneplateTheequationhasanidenticalformtothatofthethin-lensequation,afactwhichisnotmerelyacoincidencesinceSisactuallyimagedinconvergingdiffractedlightatP.Accordingly,theprimaryfocallengthissaidtobeTheFresnelZoneplateDiscussionThezoneplatewillshowextensivechromaticaberration.Advantagesofzoneplateasalens:forUV-light,softX-rays……3。波帶片具有面積大、輕便、可折疊等透鏡不具備的優(yōu)點(diǎn)。相同點(diǎn)：都能會(huì)聚光能量5）Thefocallengthequation焦距公式：

6）Besidetheprimaryfocalpoint,additionalhigher-orderfocalpointswillexistatf1/3,f1/5,f1/7,etc.

Therealandvirtualfocalpoint

實(shí)焦點(diǎn)和虛焦點(diǎn)Therealfocalpoint

：虛焦點(diǎn)：Thevirtualfocalpoint8.2.1Thesingleslit8.2FraunhoferDiffractionAccordingtotheFresnel-Kirchhoffdiffractionformula

傍軸條件下，菲涅爾-基爾霍夫公式Q:at∑anypointfromxThesingleslitWhen，，，記憶8.2.4TherectangularapertureAmonochromaticplanwavepropa-gatinginz-directionisincidentontheopaquediffractingscreenFraunhoferDiffraction，Let:

Weget:

When

So:

,Where:

TheSingle-slitDiffractionFactor(單縫衍射因子).FraunhoferDiffraction---ThesingleslitIrradiancedistributionprincipalmaximumsubsidiary

maximaIrradiance(minima)a=±jp，or，k=1,2,3,

···

I(P)=0=Imin；Irradiance(subsidiary

maxima)

：

.

Irradiance(principalmaximum)：a=0，或q=0；I(P)=I(P0)=Imax記憶Fraunhoferdiffractionpatternofsingleslitx=ax=tana1.43p2.46p-2.46p-1.43p2p0-pp3p-3p-2p0aa0=0，sinq=0；a1=±1.43p，sinq=±1.43l/a≈±3l/2a；a2=±2.46p，sinq=±2.46l/a≈±5l/2a；a3=±3.47p，sinq=±3.47l/a≈±7l/2a。Intersectionofthetwocurves:So：

subsidiary

maximaAplotofthefluxdensityIrradianceprincipalmaximumirradiancesubsidiarymaxima......008.0017.0047.00.1)0(/)(......4707.34590.24303.10000.0IIppp±±±1.Thesubsidiary

maximum

angularwidth(次極強(qiáng)亮斑的角寬度)和零級(jí)斑的半角寬-----theangularbetweenadjacentminima相鄰暗斑的角距離Theangularandlinewidthoffringes

(條紋間距與角寬度)記憶Thehalfanglewidth：

Thehalflinearwidth半線寬為：

零級(jí)斑的角寬度比次極強(qiáng)亮斑的角寬度大一倍。2.Thehalfanglewidthoftheprincipalmaximum(零級(jí)斑的半角寬)Dq0Dx'0Dx'jSince3.Discussion

是衍射效應(yīng)強(qiáng)弱的標(biāo)志波長(zhǎng)一定時(shí)，縫寬越小，越大,衍射效應(yīng)越強(qiáng)。反之：時(shí)，此時(shí)光束沿直線傳播?？p寬一定時(shí)，波長(zhǎng)越長(zhǎng)，衍射效應(yīng)越顯著。波長(zhǎng)越短，衍射效應(yīng)越小。幾何光學(xué)就是的極限。Thepatterninthex-,y-directionsvariesinverselywiththex-,y-aperturedimensions.Ahorizontal,rectangularopeningwillproduceapatternwithaverticalrectangleatitscenter.FortherectangularapertureIfthesourceemitswhitlight,onlyintheregionabout=0willalloftheconstituentcolorsoverlaptoyieldWhitelight.Anarrowsingleslit(inair)inanopaquescreenisilluminatedbyinfraredfromaHe-Nelaserat1152.2nm,anditisfoundthatthecenterofthetenthdarkbandintheFraunhoferpatternliesatanangleof6.20offthecentralaxis.Pleasedeterminethewidthoftheslit.Atwhatanglewillthetenthminimumappeariftheentirearrangementisimmersedinwater(nw=1.33)ratherthanair(na=1.00029)?Thesingleslitdiffractionwithalinesource衍射圖樣為直線條紋，是無(wú)數(shù)點(diǎn)光源形成的衍射圖樣非相干(manyincoherencepointsource)疊加的結(jié)果。8.2.5ThecircularaperturePlanewavesimpingingonascreencontainingacircularapertureandtheconsequentfar-fielddiffractionpatternspreadacrossadistantobservingscreen.Byusingafocusinglens,canbebroughtinclosetotheaperturewithoutchangingthepattern.Obviously,thisisthesameprocessthattakesplaceintheeye,atelescopeorcameralens.FraunhoferDiffraction8.2.5TheCircularAperture(夫瑯禾費(fèi)圓孔衍射)1）TheIrradiance

：Theapertureradius

，Diffractionangle：thefirstorderBesselfunction一階貝塞耳函數(shù)

Theirradiancewithθis

Thecentermaximum

：x=0，q=0Irradiancedistribution0.51.0[2J1(x)/x]2x/2p00.611.121.62-0.61-1.12-1.62Thesubsidiary

maximum

：

sinq1'=0.819l/asinq2'=1.333l/asinq3'=1.84l/a

Theminima：

sinq1=0.610l/asinq2=1.116l/asinq3=1.619l/aThediffractionpatternDiscussion1.AiryDiskBecauseoftheaxialsymmetry,thetoweringcentralmaximumcorres-pondstoahigh-irradiancecircularspot,knowasAirydiskFraunhoferDiffractionTheangleradiusoftheAiryDisk愛里斑：TheaperturediameterExample:AHe-Nelaser

,ThediameteroftheexitofHe-Nelaseris1mm,findthediffractionangleofthelaserbeam

(TheangleradiusoftheAiryDisk)？Atthedistanceof

10km,ThediameteroftheAirydiskcanreach7.7mIfisthecorrespondingangularmeasureoftheAirydisk,then

記憶FraunhoferDiffraction0.5mmholediameter1.0mmholediameterIntheveryfinestlenses,whereaberrationshavebeenmadenegligible,thespreadingoutofeachimagepointduetodiffractionrepresentstheultimatelimitonimagequality.Weexaminethesimplifiedmatters,twoequalirradiance,incoherent,distantpointsources,forexample,twostarsseenthroughtheobjectivelensofatelescope.8.2.6Resolutionofimagingsystems光學(xué)儀器的像分辨本領(lǐng)Resolutionofimagingsystems1.Examiningtwoequal-irradiance,incoherentdistantpointsources兩個(gè)非相干物點(diǎn)形成的衍射斑

Overlappingimages（3）Theminimumresolvableangularseparation-------Rayleigh’scriterion

:Theangularseparationofthestars：Theangularhalf–widthofthestarWhen，F(xiàn)ig.（a）theimageswillbedistinct.

When，F(xiàn)ig.（c），Undistinct記憶When,Fig.（b），Theminimumresolvableangularseparation

TheconditionRayleigh’scriterion()min==1.22/D(稱為儀器的最小分辨角)TheminimumresolvableangularAsthestarsapproacheachothertheirrespectiveimagescometogether,overlapandcommingleintoasingleblendoffringes.AdoptingLordRayleigh’scriterion,thestarsaresaidtobejustresolvedwhenthecenterofoneAirydiskfallsonthefirstminimumoftheAirypatternoftheother,Theminimumresolvableangularseparation

or

angularlimitofresolutionis=1.22/DRayleigh’scriterion記憶()min==1.22/DRayleigh’scriterionTheminimumresolvableangular

HowtoreducethesmallestresolvableseparationbetweenimagesByusingwavewithsmallerwavelength,forexamples,UVlight,orelectrons(equivalentwavelengthsofabout10-4to10-5thatoflight)Increasethediameteroftheobjectivelensormirror.ThehumaneyeLettakethepupildiameterofthehumaneyeunderbrightconditionstobeabout2mm,with=550nmWithafocallengthofabout20mm,thediameterontheretinais14μm.Example:Atelescopehasanobjectivelenswitha5cmdiameter.Determineitsangularlimitofresolutionatawavelength550nm.Solution：

Telescope已知望遠(yuǎn)物鏡的直徑D=5cm，白光的平均波長(zhǎng)為，求望遠(yuǎn)鏡的最小分辨角和剛剛能夠被人眼分辨兩個(gè)物點(diǎn)所需的視角放大率M?解：（1）（2）望遠(yuǎn)鏡的物鏡和目鏡的作用望遠(yuǎn)鏡的物鏡是孔徑光闌，限制入射光束的孔徑角，具有衍射作用。目鏡:其作用是放大衍射斑的視角。LoFLe8.2.3DiffractionbymanyslitsNlong,parallel,narrowslitseachofwidthaandcenter-to-centerseparationd.縫寬a(widthofeachslit)andcenter-to-centerseparation(縫距)d(相鄰縫對(duì)應(yīng)位置)Singleslitdiffraction(a)Theinterferenceofmanyslits縫間干涉(d,N)每相鄰光束間有確定光程差)ThephasedifferenceDiffractionbymanyslitsOpticalPathDifferenceintheadjacentslit(

Thetotalcomplexamplitude(復(fù)振幅疊加法)Thesameamplitude，ThetotalWhereTheOPLfromPtothecenteroftheslits(整個(gè)光柵中心到觀察點(diǎn)P的光程)，，TheirradiancedistributionfunctionisThediffractioneffect衍射因子

：Theinterferenceeffect干涉因子

記憶Discussion1.Theprincipalmaximawhen記憶主極大Zero-orderprincipalmaximumThenumberofprincipalmaximaWhen觀測(cè)條紋考慮缺級(jí)2.Minimaofzeroflux-densityExistwhenever(sinNβ/sinβ)=0orwhenBetweenconsecutiveprincipalmaxima(i.e.,overtherangeinof),therewillbeN-1Minimaand

N-2subsidiarymaxima。

FraunhoferDiffraction極小Thehalfwidthofangularfortheprincipalmaxima(主極強(qiáng)的半角寬度)From

中央主極強(qiáng)的半角寬度：

When記憶4．Theeffectofthesinglediffractionfactor單縫衍射因子的作用When：（maximum）5.MissingOrders(缺級(jí)).MissingOrders：，，記憶Example:Alightbeamwithwavelengthλ=600nmisnormallyincidentonatransmissiongratingandaFraunhoferdiffractionpatterncanbeobservedonascreen.Thesecondprincipalmaximumoflightisnotedatandthethirdorderprincipalmaximumismissing.Find(1)thegratingconstant;(2)thepossiblesmallestwidthofslit;(3)andlistallthediffractionspectraonthescreen.記憶ThediffractiongratingArepetitivearrayofdiffractingelements,eitheraperturesorobstacles,whichhastheeffectofproducingperiodicalterationsinthephase,amplitude,orboth,ofanemergentwaveissaidtobeadiffractiongrating.8.2.8ThediffractiongratingTransmissionGratingDiffractionGratingTransmissionAmplitudeGratingTransmissionPhaseGratingReflectionGratingReflectionAmplitudeGratingReflectionPhaseGratingGratingequationfornormalincidencedsinθbright=mλm=0,1,2,…TheintegermistheordernumberofthediffractionpatternIftheincidentradiationcontainsseveralwave-lengths,eachwavelengthdeviatesthroughaspecificangleDiffractionGratingThegratingequationisdependentandso,foranyvalueofm0thevariouscoloredimagesofthesourcecorrespondingtoslightlydifferentangles(m),spreadoutintoacontinuousspectrum.Noticethatthesmallerdbecomesingratingequation,thefewerwillbethenumberofvisibleorder.DiffractionGratingDiffractionGratingm=0m=1m=2m=-1m=-2GratingGratingequation

Considerthegeneralsituationofobliqueincidence.Thegratingequation,forbothtransmissionandreflection,becomesDiffractionGratingwheremisinteger.

TransmissionAmplitudeGratingDiffractionGratingGratingequationForobliqueincidenceDiffractionGratingReflectionAmplitudeGratingDiffractionGratingGratingequationFornormalincidenceForobliqueincidence光柵方程Thegratingequationisdependentandso,foranyvalueofm0thevariouscoloredimagesofthesourcecorrespondingtoslightlydifferentangles(),spreadoutintoacontinuousspectrum.Noticethatthesmallerdbecomesingratingequation,thefewerwillbethenumberofvisibleorder.DiffractionGratingN=2N=3N=16N=7GratingspectrometerTheworkingprincipleFromthegrattingequationGratingspectrometer(光柵光譜儀)

Thegratingequationisdependentandso,foranyvalueofm0thevariouscoloredimagesofthesourcecorrespondingtoslightlydifferentangles(),spreadoutintoacontinuousspectrum.Theangulardispersionpower光柵的色散本領(lǐng)Thedifferenceinangularpositioncorrespondingtoadifferenceinwavelength兩條譜線中心的波長(zhǎng)間隔與被分開的角距離或在屏幕上被分開的線距離之比分別稱為角色散本領(lǐng)和線色散本領(lǐng)。，Theangular(orlinear)dispersionformula角色散本領(lǐng)和線色散本領(lǐng)公式3）Discussion（1）（2）（3）and

areindependentofN記憶4）Example：Solution:（1）AsodiumlamphastwoyellowcomponentsatAnd.Usingadiffractiongrating15cmwide,with1200linespermillimeter.Pleasefind(1)theposition,thehalfwidthofangularinthefirstorder.(2)angularseparationofthetwolines‘sinthefirstorder.

（2）

Rayleigh’scriterion瑞利準(zhǔn)則(b)?(a)Thechromaticresolvingpower色分辨本領(lǐng)：譜線的半角寬度(Half-widthangular)AccordingtoRayleighcriterionThechromaticresolvingpowerThechromaticresolvingpower光柵色分辨本領(lǐng)記憶Example:forasodiumlamp1=5890,2=+=5896

(k=2,N=491),(k=3,N=327)Freespectralrange(自由光譜范圍)記憶BlazedgratingForareflectedoratransmittedmulti-slitgrating,mostoftheincidentlightpropagatesalongthedirectionofzerothorder,i.e.thedirectioninthegeometricoptics.Itmeansmostoftheincidentdoesnotundergodeflectionandthelight.isessentiallywasted,atleastforspectroscopicpurposes.BlazedGratingInablazedgrating,thediffractiongratinggroovesarecontrolledtoformrighttriangleswitha"blazeangle”.Intheblazedgrating,thestrongestpeakisnotthe0thorder.DiffractionGratingBlazedgratingcanenhancetheenergyofacertainorderofdiffraction.ABlazedgratingisdecidedbytheblazedangleg,thegratingspacea,theblazedwavelength,andsoon.qiqrq0dgspecular0thTheSpecularreflectionhappensatDiffractionGratingDdqbqb-qb垂直于面入射閃耀波長(zhǎng)：b；閃耀級(jí)次：j。【閃耀光柵的特點(diǎn)】：?jiǎn)尾蹖挾萢與刻槽間距d相差很小，故其它衍射級(jí)次（包括中央0級(jí)）都因幾乎落在單槽衍射的極小值位置而形成缺級(jí)，從而將80%～90%的光能量都集中到b成分的第j級(jí)譜線上?！窘Y(jié)論】：滿足閃耀條件時(shí)，波長(zhǎng)b的第j級(jí)譜線將被轉(zhuǎn)移到單槽衍射