Proficiencyin Makingfine Adjustments of Opticalcomponents

EOP3056OpticalMetrologyandTestingExperimentOM1:IntroductiontoMichelsonInterferometer

1.0 Objectives

To construct aMichelson interferometer from discreteoptical componentsTo explain how Michelson'sinterferometerproducedaninterference pattern.To analyze theMichelson interferometer behaviors and characteristicsPractice in takingclear and intelligible laboratorynotes

Proficiencyin makingfine adjustments of opticalcomponents

2.0 Apparatus(number in the brackets is the numberof sets)Opticalbreadboard (1)

1.5mWHeNelaserwithmountingassembly(1)

Beam steeringmirrorwith mountingassembly(4)

Bi-concave lens, f =-25.4 mm, with mountingassembly(1)Bi-convexlens, f= +200mm, with mountingassembly(1)

Broad band beam splitter, R/T 50/50@ =480– 700 nm,AOI= 45o,withmountingassembly(1)

Beam stop (2) and viewingscreen(1)

2 mm plastic aperture(1) and 2 mm paperapertures (2)

Plastic ruler(1) andcardboard marked with 90overtical line (1)Rotation stage mountedwith a microscope slide(1)

Aluminium coatedmicroscope slidewith mountingassembly(1)

3.0 Introduction

TheMichelsoninterferometerisanimportantexampleofinterferometersbasedondivisionofamplitude.Apartiallyreflectingmirrorisusedtodivideawave(beam)intotworesultingwaves(beams)whichwavefronts(beamsizes)maintaintheoriginalwidthbuthavereducedamplitudes.Thesetwobeamsaresentinquitedifferentdirectionsagainstplane mirrors,fromwheretheyare broughttogether again to forminterference fringes.

Figure 1: TheMichelson interferometer.

Sisalightsource.Lisadiffusingground-grassplateoralenstoextendthesmalllightsourceS.BSisapartiallyreflectingmirrororbeamsplitter.M1andM2arehighlypolishedplanemirrors.Cisacompensatingplatewhichisidentical to BSexcept thepartiallyreflectingcoating.

The Michelsoninterferometerhadbeeninventedbeforethefirstrubylaserwasbuilton1960.Anextendedlightsourceisrequiredtoextendthefieldofviewofanobserver.Forsmalllightsource,anextenderLisrequired.ThelightcomingfromthesourceSisdividedinto(1)areflectedand(2)atransmittedbeamofequalintensitybythebeamsplitter.ThesetwobeamsarereflectedbymirrorsM1andM2 andreturntothebeamsplitter.PartofthebeamcomingfromM1passesthroughthebeamsplitterandpartofthebeamcomingfromM2isreflectedbythebeamsplitter.Thus,thetwobeamsarebroughttogethertoforminterferencefringes.

SinceonebeampassesthroughBS3times,acompensatingplateCisrequiredforanotherbeamsothatbothbeamspassthroughequalthicknessofglass.Theinclusionofacompensatingplatenegatestheeffectofdispersion(opticalpathvaryingwithwavelength)duetotheglassmediumofthebeamsplitter.Hence,averyboardbandwidthsourcecangeneratefringes.However,Cisnotrequirediflasersourceisused.Toobtainfringes,themirrorsM1andM2are made exactlyorcloselyperpendiculartoeachother.Depending onthebandwidth(coherency)ofthesource,theopticaldistanceofM1andM2tothepartiallyreflectingcoatingmustbecloselyequal.However,ifalasersourceisused,opticalpathdifference up to 10 cmcan still produce fringes.

3.1 Circularfringes

To understand the originofthe fringesformed,Figure 1 is redrawnwith all the elements in astraight line.

Figure 2: Aconceptualrearrangement of theMichelsoninterferometer

ObistheobserverviewingatBSwherealltheelementscanbeseeninBS.M2’istheimageofM2formedbyreflectioninBS.AssumethedistanceofM2toBSislargerthanthatofM1to BSandM1andM2’areparallel.LisswungoveraboutBSsothatitisinlinewithM1andBS.L1’andL2’aretheimagesofLinM1andM2’,respectively.AlargecollectinglenscanbeputatDepositiontoformfringesonascreen locatedat thefocal plane of thelens.

Fromthefigure,thetwovirtualsourcesL1’andL2’arecoherentinthatthephasesofcorrespondingpointsinthetwovirtualsourcesareexactlythesameatallinstants.IfdistheseparationofM1 andM2,theseparationofL1’andL2’is2d.Whendisexactlyanintegralnumberofhalfwavelengths,allraysoflightreflectednormaltothemirrorswillbeinphase.However,rays of lightreflectedatananglewill not in phase in general.

ConsiderasinglepointsourcePonLemittinglightinalldirections(thesamefromP1’andP2’).LetarayfromPreflectedatananglebyM1andM2’toformtworays(actuallyformedbyBS).SinceM1andM2’areparallel,thetworaysarealsoparallel.ThepathdifferencebetweenthetworayscomingtotheobserverfromcorrespondingpointsP1’andP2’ withanangle to theopticalaxis is 2dCos.

Hence,itcanbegeneralizedthatsplitparallelrayswillreinforceeachothertoproducemaximumintensity(constructiveinterference)fringesforthoseanglessatisfyingtherelation

2dCos=m------Eq. 1

wheremisanintegerandisthewavelength.Foragivend,mand,isconstant,constructiveinterferencewilllieintheformofcircleswiththeircentersontheopticalaxis,whicheachis correspondingto an m value.

Theintensitydistribution across the ringsisgiven by

IA2=4a2cos2(/2)----- Eq. 2

whereaistheamplitudeofthesplitwaves,Aisthatoftheirresultantandisthephasedifferencegivenby

=(2/)*2dCos------Eq. 3

Fringesofthiskind,whereparallelbeamsarebroughttointerferencewithphasedifferencedeterminedbythe angleofinclination ,areoftenreferred toasfringes of equal inclination.

Aparticularringcorrespondstoafixedorderm.AsM2’ismovedtowardM1,ddecreases,fromEq.1,Cosincreasesandthereforedecreases.Hence,theringsshrinktowardthecenter,withthehighest-orderone(Cos=1)disappearingwheneverddecreasesby/2.Eachremainingringbroadensasmoreandmorefringesvanishatthecenter,untilonlyafewfringesfillthewholefieldofview.Bythetimedisequaltozero,thecenterfringewillhavespreadout,fillingtheentire fieldof view.WhenM2’isfurther moved,fringesreappearatthecenterand move outward.

3.2 Fringes ofequalthickness

IfthemirrorM2’andM1arenotexactlyparallel,fringeswillstillbeseenwithmonochromaticlight.In this case the space between the mirrors is wedge-shaped.

Figure 3: The formation offringes with inclinedmirrors inthe Michelsoninterferometer

ThetworaysreachingtheobserverObfromapointPonthesourcearenotnolongerparallel,butappeartodivergefromapointP’nearthemirrors(notetheschematicisdrawnnot in scale).For variouspositions of P on theextendedsource,it canbeshowed that the pathdifferencebetweenthetworaysremainsconstantbutthatthedistanceofP’fromthemirrorschanges.Iftheanglebetweenthemirrorsisnottoosmall,thedistanceofP’fromthemirrorsisnotgreat.Ifthedistancebetweenthemirrors,d=0,thefringesarestraightbecausethevariationofthepathdifferenceacrossthefieldofviewisdueprimarilytothevariationofthethicknessoftheair-filmbetweenthemirrors.Withawedge-shapedfilm,thelocusofpointsofequalthicknessisastraightlineparalleltotheedgeofthewedge.Ifdhasanappreciablevalue,thefringesarenotexactlystraightbecausethereisalsosomevariationofthepathdifferencewithangleasmentionedinsection3.1.Theyareingeneralcurvedandarealwaysconvextowardthethinedgeofthewedge.Ifdisdecreased(M2’movestowardsM1withoutchangingtheinclinationofM2’),thefringeswillmoveto‘curve-in’side,anewfringecrossingthecentereachtimedchangesby/2.Whendapproaches0,thefringesbecomestraighteruntilwhend=0,M2’intersectsM1,thefringesareperfectlystraight.WhenM2’movesfurther,thefringescurveintheoppositedirection.Forlargepathdifferences,larged,thefringescannotbeseen.Becausetheprincipalvariationofpathdifferenceresultsfromachange of the thicknessd, thesefringes havebeentermedfringesofequal thickness.

3.3 Application

TheMichelsoninterferometercanbeusedformanyapplications.Itisanon-contactmeasuringtechniqueviatheobservationoftheinterference/fringepatternorthefringetransition.Theequationm=2disoftenusedforvarioustypesofmeasurements.Inmostcases,distobemeasured.Measurementexamplesarewavelengthoflightsource,displacementofobject,thicknessofthinfilm,refractiveindexoftransparentsolid/liquid/gas,surfaceflatness/qualityofopticalcomponents,thermalexpansioncoefficientofsolid,pulseduration of pico/femto-secondlightpulse,and vibration frequencyof object.

3.4 Measurement of refractiveindex oftransparent solid

Thewavelength of alight is shortenedwhen it propagates in a transparentmaterial,

=o/n ------Eq. 4

,whereoisthewavelengthofthelightinvacuumandnistherefractiveindexofthematerialwhichisafunctionofwavelength,n(o).Ifamaterialhasthicknessd=m,wheremisapositiveinteger,thend=m*o/nandhencend=mo,wherendistheopticalpathlengthofthelightwitho,i.e.thepathlengthpassedbythelightinvacuum.InMichelsoninterferometer, both interference beams propagatein theirinterferometerarms twice,hence

mo=2nad ------Eq. 5

,wherenaistherefractiveindexofairanddisthedistancebetweenthetwointerferometerarmmirrors. 2nad is the optical path lengthdifference between the two interference beams.

TomeasuretherefractiveindexofatransparentsolidwithaMichelsoninterferometer,itisnecessarytoslowlyvarythelengthofthesolidthroughwhichtheinterferencebeampassessothatthenumberoffringesshiftedontheviewingscreencanbecounted.Atechniqueisusedforsuchmeasurement.Figure1showsthearrangementoftheMichelsoninterferometerwithatransparentsolidlocatedatonearmoftheinterferometer.Astheplateisrotatedfrom0otoanangle,thelightpassesthroughagreaterpathlengthinthetransparentmaterial.This shifts a number offringes on theviewingscreen.

Figure4:Michelsoninterferometerarrangementforthemeasurementoftherefractiveindexofatransparentsolid.ThenotationsS,L,BS,M1andM2arethesameasgiveninExperimentOM1,Figure1.ThesampleisrotatedaboutthepointOfrom0oto.b1isthebeampathwhenthesampleat0owhileb2isthebeampathwhenthesampleatangle.Thepathlengthofthebeaminthesampleisincreasedfromttoawhileitspathlengthinairisdecreasedby (c–t),wheretisthethicknessofthe sample.

Toderiveanequationforcalculatingtherefractiveindexofatransparentsolidwiththemeasuredandthenumber offringesshifted(N),considertheplateisrotatedaboutthepointO in Figure1.

When the plate is at0o:

Base onequation Eq. 2,

m1o2nala12nglg1

------Eq. 6

,wherengistherefractiveindexofthesample,la1isthepathlengthinairandlg1isthepath

lengthin thesample.interference beams.

2nala12nglg1

istheopticalpathlengthdifferencebetweenthe

When the plate is atdegrees(This rotation shifts anumberof fringes):

From Eq.6 and Eq.7:

m2o2nala22nglg2

------Eq. 7

(m2m1)oNo2na(la2la1)2ng(lg2lg1)

------Eq. 8

, wherem2–m1=Nisthe numberoffringesshifted,la2la1isthe pathlengthchange inairandlg2lg1isthepathlengthchangeinthesample.

Togetlg2lg1,considerthetriangularOPQ,where OP=t=lg1,OQ = a = lg2andPQ=b,

lg2lg1=a–t ------Eq.9

Togetla2la1,considerthe triangularOQR,where OR= c,

la2la1= –(c –t)=t–c ------Eq.10

Thenegativesignfor(c–t)isincludedbecausethepathlengthpassedbythebeamthroughair is reducedby(c – t)as shown in Figure1.

Afterthederivationofequationsforaandc,substitutionintoEq.9andEq.10andthenintoEq.8with na=1, the refractive indexequation is

(2tN

)(1Cos)N

2o2

ng 

o4t

2t(1Cos) No

---- Eq. 11

, wherethe term N2o /4tis negligible for visiblewavelengths andmaybe ignored.

Notethatna=1.000293atstandardtemperature(0oC)andpressure(1atm)foro=589.29nm(Sodium Dlight).Itisreasonabletotake n=1.0003atroomtemperature and1atmforo

=632.8 nm (HeNe laser redlight).

4.0 Warnings andprecautions

Studentsare responsible to becareful the below warnings andprecautions.Studentsare responsible to own and other personal safety.

4.1Lasersafety

Thehelium-neon(HeNe)laserusedisaclassIIIalaserwhichcancausepermanentdamagetoyourvision(retina).Neverlookatadirectlaserbeamoradirectreflectionofalaserbeamfromaspecular(mirror,glass,metal,etc.)surface.Neverputyoureyesattheplanewherealaserbeamisguidedtotraversebyopticalcomponents.Donotwearrings,watchesorothershinyjewelrywhenworkingwithlasers.(Alltheseobjectscouldsendlaserbeamstowardsyoureyesorthoseotherpersonsnearby).Neverinsertanopticalcomponentdirectlyintoalaserbeam(toavoidanypossiblebeamreflectionsfromthecomponent,e.g.fromthechamfersofthecomponent).Neversimplyflipanopticalcomponentinalaserbeam(toavoidanypossiblebeamreflectionsfromotherspecularobjectslocatedwithinthesameworkspace).Useonlydiffusereflectors(e.g.roughsurfacewhitepapers)forviewingortracingHeNelaserbeam.Alwaysblocklaserbeamclosetothelaserwhentheexperimentisleftunattended.

4.2Partial and diffusereflections oflaserbeam

Inadarkenedroom,ourpupilswillbeexpandedandwillletin60timesmorelightthaninalightedroom.Thisexperimenthasmanypartialreflections(fromlens,transparentapertures,anti-reflectionsurfaceofabeamsplitter)anddiffusereflections(fromvariousobjects:viewingscreen,holders,mounts,posts,etc.)Hence,thisexperimentwillbeperformedinalightedroom.Furthermore,thelightintensityofthefringesontheviewingscreenissufficientlyhigh to be viewed in lightedroom.

4.3Tracing laserbeam

Anexperimentnormallyinvolvesmorethanoneopticalcomponentandmechanicalpartwhichcangivetotalorpartialreflectionsoflaserbeam.Itisalwaysrequiredtoknowalaserbeamdirectionandposition.Tracingtechniqueisalwaysused.Todothistracing,putabeamstop(aroughsurfacewhitepaperforHeNelaser)atapositionwherealaserbeamdirectionandpositionareknownandmovethebeamstopawayinthelaserbeamdirectionuntil to the desireddistance or location.

4.4Handlingopticalcomponents

Theopticalcomponentsusedareexpensive.Nevertouchtheopticalsurfacesoflenses,mirrors,beamsplitters,etcwithyourskin(finger,nose,etc.)oranyobjects(exceptlenstissues).Thecoatingsonthesurfacescanbedegradedbythefattyacidsofhumangreaseorscratchedbytheobjects.Itisthesameoftheairblownoutfromhumanmouthwhichcontainsacidicmoisture.Inthisexperiment,alltheopticalcomponentshavebeenmountedontheirholderswithmountingposts,alwayscarrytheopticalcomponentsatthemounting posts. Neverremovethe opticalcomponentsfromtheirholders.

4.5Adjustment knobs ofadjustablemirrormounts

Neverturnanadjustmentknobofamirrormountmorethanafewturns.Itshouldneverbefarfromitsmediumposition.Thespringofthemirrormountcouldbedamagedifitisoverstretched.

4.6Clampingscrews

Thereareclampingscrewsonthepostholderandthelasermountingassembly.Donotovertightenthesescrews.Thismaydamagethescrewthreadorbreakthemechanicalclampingparts.Instead,tightenthescrewsuntiltheholdersaresufficienttoholdtherequiredpartswithoutmoving.E.g.tightentheclampingscrewofapostholderuntilitisjustsufficienttoholditsmountingpostwithoutslidingdown.Notethattherequiredstrengthfortighteningaclampingscrewdependson the load to be held without moving.

4.7No rush work

Youareadvisednottocarryoutthisexperimentinrushtoavoidanymistakeswhichcouldcausethedamagesasmentionedpreviously,especiallyyoureyes.Asanexample,acuttingofamountingpostacrossalaserbeammay sendareflectedlaserbeamtowardsyouroryourco-worker’seyes.Althoughthelaserbeamsweepsacrossyoureyesinashortinstant,itmaytemporarilycause a‘dark line’ existing inyourvision.

5.0 Experiment

Figure 5:Schematic viewofMichelsonInterferometer.

Themountingassembliesofthecomponentsarenotshownintheschematicdiagram.M1,M2,M3andM4arethebeamsteeringmirrors.L1isthebi-concavelensandL2isthebi-convexlens.BSisthebeamsplitter,whereS1isthebeamsplittingsurfaceandS2istheanti-reflectionsurface.BSBisthebeamstopforblockinglaserbeamclosetothelaser.A1,A2,A3,A4,A5andA6aretheapertureorbeam-stoplocationsalongthesetupoftheMichelsoninterferometer.Thenumbersattheoutsideoftheopticalbreadboardindicatethedistancesininches.Thedistancebetweenadjacentscrewholesisoneinch.Theadjustablemirrormounthastwofinethreadscrewsforadjustment,asteelballandtwopullingsprings.

Theexperimentalproceduresbelowonlyincludetheimportantsteps(includingthesafetysteps)forcarryingoutthisexperiment.Theydonotcontainallthedetailsontheadjustmentandalignmentofthelaserbeam.Youneedtothinkandfeelonthem,e.g.howmuchandhowlighttoturnanadjustmentknobofamirrormountforasmallbeammovementintherequireddirection. Thebelow aremechanical parts foroptical alignment.

i.Laser mounting assembly:

a.Laser tubeheight: slidepost clamp up/down along its mountingpost

b.Laser tubehorizontal tilting:rotate postclamp about its mountingpost

Loosethepostclampingscrewalittlebit(don’tloosetoomuch)formovement.Donotover-tightentheclampingscrew.Laser tubevertical tiltingis not allowed.

ii.Adjustablemirror mount:

a.Laserbeam horizontal finesteering(X): turn thehorizontal fineadjustmentscrew

b.Laserbeamvertical finesteering(Y):turn the vertical fine adjustment screw

iii.Mountingpost and its post holder

a.Laserbeam horizontal coarsesteering(X):rotate themountingpost in its post holder

b.Opticalcomponent height: slidethe mountingpost up/down in its post holder

Loosethepostholderclampingscrewformovement.Donotover-tightentheclampingscrew.Laserbeamverticalcoarsesteering(Y)isnotallowed.Theopticalcomponentherecan bemirror, lens,beamsplitter,etc.

iv.2 mm aperture:

Itisalwaysusefulforopticalalignmenttomarklaserbeamcenterortheopticalaxesofopticalcomponentsandtoactasascreentomonitorthereflectionsfromopticalcomponentsthatare inserted in the beamafter the aperture.

Studentmustreadandunderstandsections4.0to4.7and5.0beforeperformingtheexperiment below.

Notethatopticalalignmentneedspatienceandtime.Youmustmakesurenottoknockdown any opticalcomponent along the opticalalignment.

Thisexperimentiscarriedoutinalightedroom.Neverswitchofftheroomlights.Ifnecessary, youmay block thelights fromthe roomlamps toreachtothe screen.

5.1Procedures forsetting up a MichelsonInterferometer

5.1.1U-shapedbeamalignment

i.ThelaserbeamwilltraverseinaU-shapedpathasshowninFigure4andinaplanewhichisparallelwiththesurfaceoftheopticalbreadboard.Hence,youshouldneverput your eyes at this lasertraversing planelevel.

ii.Makesurethelaserisnotturnedon.RemoveL1,L2,BSandalltheaperturesfromthe laserbeam path.

iii.Laserisstilloff.Checkthedirectionsofthelaseroutput,M1andM2 sothatwhenthelaseristurnedon,thelaserbeamwilltraverseapproximatelyinaU-shapedpath.Using aplasticruler,checkwhether thecenter-heightsofthelaseroutput,M1andM2areabout12cm.Ifnecessary,correspondinglyadjustthemountingassembliesofthelaser(donotloosetheclampingscrewtoomuch,elsetheclampwillslidedown),M1andM2.(Note:normally,theyareinthecorrectpositionsunlesssomeonehasmovedtheir positions.)

iv.Laserisstilloff.Putabeamstop(BSToraroughsurfacewhitepaper)closetothelaser.Turnonthelaser.TracethelaserbeamuntilapositionclosetoM1.(NotethatifyouaresuretheapproximatepositionofthelaserbeamclosetoM1,youmayputBSTdirectlyclosetoM1.)WiththelaserbeamfallingonBST,makesureM1cancapturethelaserbeamifBSTisremoved.Adjustthelasermountingassemblyif

necessary.Putanotherbeamstop(BSB)closetothelaser(toblockthelaserbeam).MoveBSTtoA2position.RemoveBSB(tounblockthelaserbeam).Checkwhetherthelaserbeamintersects M1 at its center. Adjust the laser mountingassemblyif necessary.

v.Notethatfromthisonwards,procedureswillbementionedinmore simpleforms,includingprecautionsteps.Itisyourresponsibilitytomakesureyoucanunderstandthemeaningsofthesimpleforms.WithBSTatA2,tracethebeamuntilM2.MakesureM2cancapturethebeam.AdjustM1mountingpostifnecessary(donotaccidentallyknockdownBST).MoveBSTtoA5(blockthebeamfirst).Usingaplasticruler,recordthecenter-heighthofthebeamjustafterM1.(Caution:Nevertouchthemirrorsurface!Thevalueh maynot bethe actualvalue.Make sureyouusethesameendoftherulertouchingthebreadboardsurfaceforothercenter-heightmeasurements).CheckwhetherthebeamintheM1-M2armintersectsM2atitscenterandhasthesamecenter-heighthjustbeforeM2.Ifnecessary,correspondinglyadjusttheadjustmentknobsandmountingpostofM1andthemountingpostofM2(don’tknockdownBST).(Foreasyalignmentsfortherestofexperiments,maketheM1-M2-armbeaminparallelwiththerightedgeofthe

breadboard.Youmayusethecardboardmarkedwith90overticallineandalineofscrewholesonthesurfaceofthebreadboardforthisparallelalignment.Notethatthebeamisnotontopofalineofscrewholesbutoffsetabout3mmfromthe center ofthescrewhole.)

vi.WithBSTatA5,tracethebeamuntilA6position.Usingthecardboardmarkedwith90overticalline,checkwhetherthebeaminM2-M4armisparalleltothefrontedgeofthebreadboard(oralineofscrewholesonthesurfaceofthebreadboard,offsetabout3mmfromscrewholecenter).ThebeamatA6musthavethesamecenter-

heighth.(Thisparallelarrangementisimportantforeasyalignmentfortherestofexperiments.)Ifnecessary,correspondinglyadjusttheadjustmentknobsandmountingpostofM2(don’tletthebeamshootoutsideBST).Now,thebeamhasbeenalignedtotraverseinaU-shapedpathandinaplaneparalleltothebreadboardsurface.

5.1.2Laserbeamexpander alignment

i.Aninvertedtelescopeisusedtoexpandalaserbeam.Inthisexperiment,Galileantelescope is used.

ii.Lensalignment:Itisimportanttoknowhowalensisalignedproperly.Therearetwopartialreflectionsfromalens,onefromeachsurface,whichformtwospotsonanaperturescreen.Inthisexperiment,thealignmentsequencesare:(1)Slideup/downthelensmountingpostuntilthespotscentersareatthesameheightoftheaperture.

(2)Slideleft/rightthepostholderuntilthetwospotsareoverlapping.(3)Rotatethepostholderuntilthetwospotsarecenteredabouttheaperture.(Notethatthelensmountingassemblydoesnotallowverticaltilting.Hence,thespotsmaynotbecoincidentatthetoporbottomoftheaperture.)Noteonthemovementsofthespotswithrespecttoeachoftheadjustments.Repeatingup/down,left/right,rotatemovements mayberequired to align the lensproperly.This alignment consumes time,dependingonindividualalignmentskill.Considergeometricalopticsofrayreflectionandrefraction.

iii.Putthe2mmplasticapertureatA1positionandalignitsothatthebeampassesitscenter.(Foreasyviewingthebeampassingtheaperturecenter,putaroughsurfacewhite paperclosetotheapertureattheexitside,theback-scatteredlaserlightwillhelpyoutoviewtheapertureopeningarea.)Puta2mmpaperaperture

atA4positionandalignitscenteratthebeamcenter.Putanother2mmpaperaperture at A2 position and align its centerat thebeamcenter.

iv.Blockthebeam.(Caution:Neverturnthelenschuckscrews!Thelenscaneasilydropoutfromthelenschuck.)PutinL1(Bi-concavelens)atabout4screw-holesdistancefromM1andalignroughlyitscenteratthebeampath.(UsethecentersofA2andA4aperturesor5.1.1vasaguideandusearulerforL1center-height.)Unblockthebeam.Usethelensalignmentguides,alignL1sothatthetransmittedbeamiscenteredonA4apertureandthetworeflectedbeamsarecenteredaboutA2aperture.(Theymaybeatthetoporbottomoftheaperture.RemovetheapertureatA2,youcanseethetwolarge-diameter,low-intensityspotsatA1.Oneofthespotmay haveconcentriccircular bright and dark rings).

v.Putthepaperaperture(initiallyatA2)atA3positionandalignitscenteratthebeamcenter.(Notethatthediffractionofthe2mmaperturemayaffectthebeamdirectionaftertheaperture.Hence,theaperturemustbeproperlycenteratthebeamcenter.TheapertureatA4isausefulreferenceforthisaperturecentering.)Blockthebeam.PutinL2(Bi-convexlens)atabout7screw-holesdistancefromL1andalignroughlyitscenteratthebeampath(includingitscenter-height).Unblockthebeam. Usethelensalignmentguides,alignL2so thatthetransmittedbeamiscenteredonA4apertureandthetworeflectedbeamsarecenteredaboutA3aperture.Withtheinformationin5.1.1vi,thebeamcenteratA6shouldbethe same position (height= h, offset about 3mm from screw holecenter).

vi.MakesureM4canreflectbackthebeamtoM2.RemoveBSTatA6.FinelyturntheM4adjustmentknobsuntilthereflected(returning)beampassesthroughA4apertureandthenA3aperture,andlastlyitscenterfallsatabout1mmfromtheedgeofeithersideofA1aperture.RemoveA3andA4aperture.CarefullymoveL2backandforthalongthebeamuntilthereturningbeamsizeatA1isthesamesizeastheincomingbeampassingthroughtheaperture.(Notethatthereturningbeammustbelocatedabout1mmfromtheedgeasthatbeforemovingthelens.Youcanuseawhitepapertodeterminetheincomingbeamsizethatpassestheaperture.)ThebeamafterL2iswellcollimated.MeasureandrecordthebeamsizesatA4,dA4= mmand A6, dA6= mm.

5.1.3Michelsoninterferometer alignment

i.Thebeamsplittingsurfaceofthebeamsplitterhasreflectance,R50%andtransmittance,T50%atwavelengths,=480–700nm(broadband)andangleofincidence,AOI=45o.Theanti-reflectionsurfaceisnottotally0%reflectance.Hence,itistiltedabout30arcminutestothebeamsplittingsurfacetoavoidinterferencedueto multiple internalreflections.

ii.PutapaperapertureatA5positionandalignitscenteratthebeamcenter.Usetheinformation in 5.1.1 vi to confirm the aperturecentering(diffraction effect).

iii.Blockthebeam.PutinBSwiththesurfacemarkedwith‘>’facingtoM4.RoughlyalignS1surfacecenter(Usetheinformationin5.1.1vi.Makesurethecenter-heightofBSisequaltoh)anditsorientation(45obetweenS1surfaceandthebeampath)sothatwhenthebeamisunblocked,partoftheincomingbeamwillbereflectedtoM3byS1surface.TheanglebetweenthereflectedbeamtoM3andtheincomingbeam from M2is roughly90o.

iv.Unblockthebeam.PerformrepeatingadjustmentofmovingtheBSbaseplatebackandforthalongtheincomingbeamfromM2androtatethebaseplateuntiltheanglebetweentheincomingbeamfromM2andthereflectedbeamtoM3iscloseorequalto90o.Atthesametime,thereflectedbeamfallsonaboutthecenterofM3.(Usethe

cardboardmarkedwith90overticalline.Theholesonthebreadboardsurfacecanhelptodetermine 90oangle.Thisalignmentconsumestime!)Afterthe90ohasbeenachieved,noteonthepositionandorientationofthebaseplaterelativetothescrewholesintheincomingbeamdirection.(Thisnotingisimportantforfollowingadjustment.)AdjustM3heightifnecessary.(Notethatthecenter-heightofthe

beamonM3maynotbeexactlyequaltohandthetransmittedbeamtoM4isnot centered. All theseare fine.)

v.RotatethemountingpostofM3ifnecessary.TurntheadjustmentscrewsofM3sothatthebeamreflectedfromM3passesthroughtheapertureatA5,thentheapertureatA2andlastlyfallsonthesameposition(about1mmfromthesameedge).(NotethatthebeaminitiallymaynotfallonthepaperoftheapertureatA4.Hence,youneedtotracethebeamwitharoughsurfacewhite papertoknowitspositionoutsidetheaperturepaper.Thealignmentconsumestimeandrequiresveryfineadjustmenttogetthefinalposition.)RemovetheapertureatA5.ThecoincidentpositionofthetwospotsonA1apertureshouldnotbechanged.Iftheyarechanged,adjustaccordinglytogetthesameposition(about1mmfromthesameedge).Atthiscoincidenceofthetwospots,aseriesofbrightanddarkfringesappearsontheviewingscreen.

vi.TheS1surfacemaynotbeatthecenterofthebeamatM3-BSdirectionafterA5apertureisremoved.PutBST(orapaperaperture)atthefrontofM4,movethebaseplatealongM3-BSdirectionuntilthespotonBSTisthebestwithoutblocking by thelenschucks.(NotethepositionofthebaseplateinM2-BSdirectionmustbethesameasnotedin5.1.3iv).(TheBShasbeenalignedinallX,YandZdirections).Theinterferometeralignmenthasbeen completed.

NotethataligningthetwobeamsonA1apertureisgoodforaquickroughalignmenttogetfringesappearingonthescreen.However,thisisonlyappliedforacollimatedorcloselycollimated beam.

5.2Procedures forobservation ofinterferometer behaviors and characteristics

i.Aftertheinterferometeralignment is completed,oneof the interferometermirrors willnot be movedanymore.Let M3 isfixed all the time. This section will observehowtheorientationandseparationofthefringeschangedwithrespecttotheorientationandtiltingangleoftheM4mirrormovements.Finelyturn(repeattoturnasmallstepandrelease)theadjustmentscrewsofM4sothatapproximatelyfivebrightfringesappearacrossthebeamonthescreen.Performthefollowingexperimentinsequence.YoumaysketchthefringeschangeaftereverymovementofM4foreasy discussion.

ii.Usearoughsurfacewhitepaper.Viewthefringesonthewhitepaperfromthescreenposition to a position close to BS.Record this observation in words.

iii.FinelyturnthehorizontaladjustmentscrewofM4clockwiseandobservethemovementofthefringesonthescreenuntilthenumberofbrightfringesisequalto2or10(dependingonthenumberdecreasingorincreasing).Recordthisobservationinwords(forfringes changed with respecttomirrormovements).

iv.FinelyturnthehorizontaladjustmentscrewofM4counter-clockwiseandobservethemovementofthefringesonthescreenuntilthenumberofbrightfringesisequalto 2 or 10. Record this observation in words.

v.TheobservationsarethesameforturningtheverticaladjustmentscrewofM4.Now,finelyturnthesetwoscrewsuntilapproximatelyfivehorizontalbrightfringes.

Drawthefringesonagraphpaperindetails(relativeseparation,thicknessandintensityofthebrightanddarkfringes).Askyourinstructortoverifyyourdrawnfringes and thefringesappearing on the screen.

vi.Byselectingthecorrectadjustmentsscrewsothatonlythenumberofhorizontalbrightfringeschangeswithoutchangingtheorientationofthefringes.Finelyturnthisadjustmentscrewclockwiseandcounter-clockwiseandobservethenumberofthebrightfringes.Makesureyouturnthescrewforthewholerangeuntilthenumberoffringesbecomesverylargeorequalsto1(or0)andthenincreasesagain.Recordthis

observationinwords.(Let0otiltingangleisassignedfor1or0numberoffringes,

clockwiseproducespositivetiltinganglesandcounter-clockwiseproducesnegativetilting angles. Record only comparative, no quantitative.)

vii.Turnthecorrectadjustmentscrewsothatthenumberoffringesbecomes1(or0)andthenturnanotheradjustmentscrewtogetapproximately5verticalbrightfringes.Recordthisobservationwithrespecttothemirrortiltingangleanddirectioninthissequence ofscrew adjustments.

viii.Turnthecorrectadjustmentscrewsothatthenumberoffringesbecomes1(or0).Atthisposition,letassignthehorizontaladjustmentscrewangleasx=0oandtheverticaladjustmentscrewangleasy=0o.Turnthehorizontaladjustmentscrewsandobservexuntilthereareabout10brightfringesonthescreen,letassignx=x1.Turntheverticaladjustmentscrewwiththesameturningangle,i.e.y=x1.Recordwhatyouobserveonthefringeschanged.Then,turntheverticaladjustmentscrewsothaty=0oandthenfurtherturnituntily=-x1.Recordwhatyouobserveonthefringeschanged.

ix.Turnthecorrectadjustmentscrewtogetapproximately5verticalbrightfringes.MoveL2closertoL1by4screw-holesdistance.AlignL2asmentionedin5.1.2.Recordthefringeschangedinwords.Turnthecorrectadjustmentscrewtobringtooneortwobrightfringes.Recordthefringeschangedinwords.Furtherturntheadjustmentscrewandalsoanotheradjustmentscrewuntilasinglespot(eitherbrightor dark) with side ring.Draw the fringes.

x.MoveL2closesttoL1butthebaseplatesofL2andL1arenottouchingeachother.PutBSTorapaperapertureatA6toalignL2.Drawthefringes.Turnoneoftheadjustmentscrewsandrecordthefringeschanged.Turnbacktheadjustmentscrewtothe previousfringes before go next step.

xi.RemoveL2fromthelaserbeampath(blockthebeamfirst).Drawthefringes.Turnoneoftheadjustmentscrewsandrecordthefringeschanged.Turnbacktheadjustmentscrew to theprevious fringes beforegonext step.

xii.RemoveL1fromthelaserbeampath(blockthebeamfirst).Drawthefringes.Turnoneof theadjustmentscrewsandrecord the fringeschanged.

Now,you should be ableto control thenumberoffringesand theirorientation, etc.

6.1Procedures for refractiveindex ofglass measurement

TheMichelsoninterferometeristobesetuptoproduceseveral(about5)concentriccircularfringesonaviewingscreen.The conditionstoproducethisfringepatternare (1)anexpandedanddiverginglaserbeamand(2)sufficientlylargeBS-M4armlengthcomparingwithBS-M3armlength(refertoFigure4ofExperimentOM1).Thisfringepatternaimsforeaseofcountingthenumberoffringesappearing/disappearingatthecenteroftheconcentriccircularfringes.

i.Figure4 ofExperiment OM1 is alwaysreferredin the followingalignment procedures.

ii.Ifnecessary,refertoSection5.1ofExperimentOM1forthedetailedalignmentprocedures.

iii.Takeprecautiononthe laserbeamduringthealignmentswhenthelaser beamisnotexpanded anddiverged.

iv.Remove the bi-concave lensL1and bi-convexlensL2.

v.Align the laser beam on the center ofthe mirror M2.

vi.AlignthelaserbeaminM2-BSarmsothatitisparalleltothefrontedgeoftheopticalbreadboard.Use the opticalbreadboard screw holes as a guide.

vii.AlignthebeamsplitterBSsothat(1)thelaserbeamfallsontheBScenterand(2)thereflectedbeamtoM3is90ototheM2-BSbeam.UsetheopticalbreadboardscrewholestolocateBSpositionbeforethe90oalignment.NoteS1surfaceisontheM2side,notonthe M4 side.

viii.AlignM3sothatthereflectedbeamfromM3iscloselycoincidentwiththeincomingbeam.It should fall on ~1 mm fromedge of either sideof theapertureA1.

ix.LocateM4sothatBS-M4armlengthis1inchlongerthanBS-M3armlength.AlignM4sothatthereflectedbeamfromM4iscoincidentwiththatfromM3ontheapertureA1paperandtheviewingscreen.Atthispoint,youcanseesomefringesontheviewingscreenand the apertureA1 paper.

x.Putthebi-concavelensL1inM1-M2armataposition4inchesfromM1andalignL1(up/down,left/right,rotate)sothatthelaserbeamfallsonthescreenwithaboutsymmetricalintensityprofile.Youcanseeatabout5concentriccircularfringeswiththeircentersat the center oftheintensityprofile.Ifnecessary,align M4 toget the center.

xi.MounttherotationstagewithamicroscopeglassplateinbetweenBSandM4withtwoclampingscrews(handtighteningisenough).Rotatetherotationstageadjustmentknobsothattheglassplatesurfaceis90otothelaserbeaminhorizontaldirection(verticaldirectioncannotbealigned).Foraccuratealignment,removeL1,putaroughsurfacewhitepaperatthefrontofM4(donottouchtheM4surfacewiththepaper),ifthe90oisachieved,allthesecondarydotsarealignedverticallywiththeprimarybrightdot.PutinL1andalignit.Thesamefringepatterncanbeseenonthescreen.Notethattheremayhaveafaintsecondaryfringepatternvisibleatthecenterofthescreen.Thisisformedbythe Fabry-Perotinterference between the front and backsurfacesof the glassplate.

xii.Recordtheanglereadingontherotationstage(r0).Thisisthe0oposition.Foraccuraterefractiveindexmeasurement,theglassplatemustbeas90oaspossibleandtheanglemust be readaspreciseas possible.

xiii.Slowlyrotatetherotationstageadjustmentknobandcount20fringetransitions(appearing/disappearingatthecenter).Readtheangleaspreciseaspossible(r20).Continueto count another20 fringe transitions and read theangle (r40).

xiv.Repeatprocedure11,12and13tomakesurethemeasurementsarecorrect.Ifthesetwosets of reading aredifferent too much. Repeatagain.

Datarecording:

r0= angle readingat the0oposition

r20= angle readingafter20 fringetransitions

r40= angle readingafteranother20 fringe transitions

Set 1:r0=

o, r20=o, r40=

o,1=r20– r0=

o, 2=r20– r0=o

Set 2:r0=

o, r20=o, r40=

o,1=r20– r0=

o, 2=r20– r0=o

Set 3:

…………

Calculations:

1.Calculate theaveragevalueof 1and2.

From Eq.8withN22/4t ignored,sincen isconstant,thethickness of theglassplatecanbe derivedand the resultantequation is given below.

t1

oN1N2(Cos1Cos2)

----- Eq. 12

2N1Cos1(1Cos2)N2(1Cos1)Cos2

whereo=632.8nm,N1=20,N2=40,1=theanglefromthe0opositiontomake20fringetransitions and 2=the angle from the 0oposition to make40 fringetransitions.(Cognitive– Analysing,Level 4)

[5 marks]

2.DeterminethethicknessoftheglassplatewithEq.12.Comparewiththetheoreticalvalue.

(Cognitive– Evaluating,Level 5)

[5 marks]

3.DeterminetherefractiveindexoftheglassplatewithEq.11(ignoreN22/4tterm).Compare with the theoreticalvalue.

(Cognitive– Evaluating,Level 5)

[5 marks]

Discussions

Analyse and discuss on the matters alongwith theexperimentsSetup of the interferometer

Experimentobservationrelated to theory

(Cognitive– Understanding,Level 2)

Conclusion

Concludebased on the discussed matters.

(Cognitive– Evaluating,Level 5)

[5marks]

MARKINGSCHEME

1.Experimentobjectives – 2%

2.Procedures,results,answers and discussions for allquestions andassignments– 45%

3.Conclusion – 3%

LABORATORYREPORT

Date ofsubmission:within 14 days afterperformingthe experiment

Place of submission:submit to the laboratorywhereyouconducted theexperimentLengthofreport: Yourdefinition. Write thenecessarythings.

Reportcontents:Report mustincludethe following:

i.Experimentobservations

ii.Discussion

iii.Conclusion

End ofLabSheet