邁克爾干涉儀測量空氣折射率

實驗四用邁克爾遜干涉儀空氣的折射率一、實驗?zāi)康挠梅蛛x的光學(xué)元件構(gòu)建一個邁克爾遜干涉儀。通過降低空氣的壓強測量其折射率。二、儀器和光學(xué)元件光學(xué)平臺；HeNe激光；調(diào)整架，35x35mm；平面鏡，30x30mm；磁性基座；分束器50:50；透鏡，f=+20mm；白屏；玻璃容器，手持氣壓泵，組合夾具，T形連接，適配器，軟管，硅管三、實驗原理借助邁克爾遜干涉儀裝置中的兩個鏡，光線被引進干涉儀。通過改變光路中容器內(nèi)氣體的壓強，推算出空氣的折射率。IftwoWaveshavingthesamefrequency° ,butdifferentamplitudesanddifferentphasesarecoincidentatonelocation,theysuperimposetoY=a?sin1-a)Y=a?sin1-a)+a?sin12-(X)2Theresultingcanbedescribedbythefollowlng:Y=A?sin-XwiththeamplitudeAwiththeamplitudeA2=aj+ +2a^^?COS8(1)andthephasedifference8andthephasedifference8=X-X122)圖2)圖2InaMichelsoninterferometer,thelightbeamissplitbyahalf-silveredglassplateintotwopartialbeams(amplitudesplitting),reflectedbytwomirrors,andagainbroughttointerferencebehindtheglassplate.Sinceonlylargeluminousspotscanexhibitcircularinterferencefringes,theIightbeamisexpandedbetweenthelaserandtheglassplatebyalensL.IfonereplacestherealmirrorM3withitsvirtualimageM3/,,Whichisformedbyreflectionbytheglassplate,apointPofthereallightsourceappearsasthepointsP/,andP"ofthevirtuallightsourcesL1andL2?Duetothedifferentlightpaths,usingthedesignationsinFig.2,2兀thephasedifferenceisgivenby:§= ?2?d?cos°人isthewavelengthofthelaserljghtused.Accordingto(1),theintensitydistributionfora1=a2=ais8(3)?A2=4?a2?cos2—(3)2Maximathusoccurwhen8isequaltoamultipleof2兀,hencewith(2)?d?cos0=m?九；m=i,2,...

i.e.therearecircularfringesforselected,fixedvaluesofm,andd,since0remainsconstant(seeFig.3).IfonealtersthepositionofthemovablemirrorM3(cf.Fig.1)suchthatd,e.g.,decreases,accordingto(4),theciroularfringediameterwouldalsodiminishsincemisindeeddefinedforthisring.Thus,aringdisappearseachtimedisreducedby九’2.Ford=0theciroularfringepatterndisappears.IfthesurfacesofmirrorsM4andM3arenotparallelinthesenseofFig.2,oneobtainscurvedfringes,whichgraduallychangeintostraightfringesatd=0.空氣衍射系數(shù)的確定Tomeasurethediffractionnofair,anair-filledcellwithplane-parallelboundariesisused.ThediffractionindexnofagasisalinearfunctionofthepressureP.ForpressureP=0anabsolutevacuumexistssothatn=1.An(5)n(P)=n(P=0)+——-P(5)APFromthemeasureddate,thedifferencequotientAn/APisfirstdetermined:(6)Ann(P+AP)一n(P)(6)APAPAP(7)Thefollowingistruefortheopticalpathlengthd:d=n(P)"s(7)Wheres=2?listhegeometriclengthoftheevacuatedcellandn(P)isthediffractionindexofthegaspresentinthechamber.listhelenghtofthegascolumnintheglasscell.ThefactthatthepathistraversedtwiceduetothereflectiononthemirrorM4istobetakenintoconsideration.Thus,byvaryingthepressureinthecellbythevalue△P,theopticalpathlengthisalteredbythequantity△d:△d=n(P+AP)?s■n(P)?s (8)onthescreenoneobservesthechangeinthecircularfringepatternwithchangeinthepressure(thecentreoftheinterferencefringepatternalternatelyshowsmaximalandminimalintensity).ProceedingfromtheambientpressurePo,oneobservestheN-foldresettingoftheinitialpositionoftheinterferencepattern(i.e.,establishmentofanintensityminimuminthering'scentre)untilaspecificpressurevaluePhasbeenreached.Achangefromminimumtominimumcorrespondstoachangeoftheopticalpathlengthbythewavelength九.BetweenthepressuresPandP+△Ptheopticalwavelengththuschangesby△d=(N(P+AP)—N(P))?入 (9)From(8)and(9)andunderconsiderationofthefactthatthecellistraversedtwicebythelight(s=2?l),itfollows:andwith(6)andAN=N(P+AP)一N(P)thefollowingresults:(10)An_ANandwith(6)andAN=N(P+AP)一N(P)thefollowingresults:(10)An_AN九 . AP AP2/四、實驗步驟1、裝置建立和調(diào)整：注：下文括號中的數(shù)字表示的坐標僅適用于開始階段的粗調(diào)。參照圖1擺放元件，使用調(diào)整鏡Ml(l,8)和鏡M2(l,4)調(diào)整光路時，光線要沿著平臺上的直線延伸。最初不需要放置分束器BS,光線直射M3(9,4),被M3反射后的光線能夠和M2上初始光點重合。然后放2-1置分束器在（6,4）,BS的鍍膜面朝向鏡M2，這樣一部分的光仍然可無阻礙的到達M3,另外的光射到M4（6,l）。d）現(xiàn)在屏SC（6,6）上出現(xiàn)兩個光點，調(diào)整M4使它們重合，此時觀測到的應(yīng)是一個輕微抖動的亮點。放置透鏡L在（1,7），屏上出現(xiàn)干涉條紋，細調(diào)M4能夠使干涉圖象為一組同心圓環(huán)。e）由公式e）由公式圖12、實驗a） 將容器c放置在（6,2.5）處，且其前后表面要和M4及BS間的光線傳播方向垂直，容器的前后表面請不要用手接觸，以保持表面光潔。b） 手持壓力泵與軟管相連，通過夾具固定在磁性基座（8.5,1.5）上，接到容器c的一個開口處，c的另一個開口端已封閉。c） 使用壓力泵改變?nèi)萜鲀?nèi)的壓強，當(dāng)壓力計的示數(shù)達到一個穩(wěn)定值后