WashingtonUniversityinSt.Louis PhysicalOpticsLab

IntroductoryPhysicsLab Summer2018

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PhysicalOpticsPre-Lab:AnIntroductiontoLight

ABitofHistory

In1704,SirIsaacNewtonpostulatedinOpticksthatlightwasmadeupoftinyparticlesthatbehavedjustlikeanyothermassiveobject,fromplanetstoprotons.Hehypothesizedthatlightisobservedtotravelinastraightlinebecauseitmovesatsuchahighspeed,justlikeaNolanRyanfastballappearstotravelinastraightlineinsteadofaparabola.Theparticlemodeloflightalsoexplainedmanyotheraspectsoflight’sbehavior,suchasreflectionandrefraction(bothofwhichdescribethewaysinwhichlightbendswhenincontactwithasurface).Newtonwasthenumberonenameinphysicsformorethantwocenturies,sowhenheespousedatheory,peoplebelievedit.Italsodidn’thurtthattheparticlemodelreadilyexplainedcommonlyobservedphenomena.Becauseofthis,theparticlemodeloflightdominateduntilThomasYoung,whoalsohelpeddeciphertheRosettaStone(boy,washeanoverachiever!),performedhisdoubleslitexperimentin1801.Thisexperimentconclusivelydemonstratedthediffractionandinterferenceoflight,whicharepropertiesthatcanonlybeexplainedbyawavemodeloflight.

ParticleorWave?

Modernquantumtheoryholdsthatlighthasbothwave-likeandparticle-likeproperties.Theactofmakinganobservationforcesthelighttodisplayitsparticleoritswaveproperties(inquantummechanics,thisiscalledcollapsingthewavefunction).Whetherlightwilldisplayitswave-likeorparticle-likepropertiesdependsontheexperimentaldesign,thewavelengthofthelight,andonthelength-scaleoftheobjectusedtoobservethelight(e.g.,theslitseparationinYoung’sdoubleslitexperiment).Whenthewavelengthoflightislarge,theslitseparationtendstobesmallerthanorcomparabletothewavelengthoflightanditswavenaturedominates.Asthewavelengthoflightdecreases,theparticlenatureoflightbeginstodominate.Intheexperimenttoday,alloftheslitsthroughwhichyouwillobservelightaresmallenoughthatyoucantreatlightpurelyasawave.Physicalphenomenathatcanbedescribedbyonlythewavenatureoflightarecommonlyreferredtoasphysicaloptics.Itismorephysicallyrealisticthandescribinglightasaray,asisdoneingeometricoptics.RefertoyourtextbookandAppendicesBandDforadditionalinformationonwaves,diffraction,interference,andpolarization.

TheStructureofThisLab

Thislabwilldealwithtwomajortopicsofphysicaloptics:polarizationandinterference.ThePre-Labwillfocusonpolarizationwhilethetimeinthelaboratorywillbespentinvestigatinginterference.

WashingtonUniversityinSt.Louis PhysicalOpticsLab

IntroductoryPhysicsLab Summer2018

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AnIntroductiontoPolarization

ThisseriesofPre-Labexerciseswillintroduceyoutopolarizationwiththeultimategoalofgainingabasicunderstandingofpolarizingsunglassesand3Dmovies.AppendixDgivesanintroductiontosomeofthehistoryandessentialmathofpolarization.Checkitout!

Youcanusethepolarizeryoureceivedinlablasttimetohelpyouanswersomeofthequestions.Ifyoudidnotreceiveapolarizer,youcanstopbythelabmanager’soffice(Crow307)andpickoneup.

Equipment

• Polarizer(seetheparagraphabove)• Sunglasses

TheStory

Onedayyoudecidetogiveyourlittlebrotheracalltocatchupandtotellhimhowmuchyou’relearninginyourintroductoryphysicsclass.Butallhewantstotalkaboutishiscurrentfavoritemovie,MutantZombiePiranhasfromOuterSpacein3D,whichheavowsisinfinitelymorethrillingthansciencecouldpossiblybe.Youbegtodiffer,andseeingawaytoreelhimin,youmentionthatmodern3Dmoviesareonlypossiblebecauseofscience–namely,polarization.Justasyouhadhoped,hetakesthebaitandasksyoutoexplainthis.Pleasedtohavecaughthisinterestandinthenumberoffish-relatedpunsyouwereabletoutilize,youtellyourbrotherthathe’llneedtostartwiththebasicsifhewantstounderstandhowmovieswork.

DoThis:Takethepolarizeryoureceivedinlablasttime(polarizersarealsoavailableinthehallwaybyCrow307orcontactyourLAI)andlookatavarietyofobjects,bothindoorsandoutdoors,asyourotatethepolarizer(clockwiseorcounterclockwise).That’swhenthemagicofthepolarizerhappens!Examplesofobjectsyoumightlookatinclude,butarenotlimitedto,yourcomputerscreen,yourphonescreen,alightbulb,thetable,yourlunch,thesun(indirectly,ofcourse!),thesky,etc.Becreative!

PL1.Listatleastthreeobjectsthatappeardifferentwhenyoulookatthemthroughapolarizerandthreethatdon’tseemtosignificantlychange.Makesureit’sclearinyourresponsewhichiswhich.Describetheeffectsapolarizerhasontheobjectsthatappeartochange.

PL2.Manysunglassesarepolarized.Basedonwhatyou’vealreadydiscoveredabouthowpolarizerschangethewaycertaintypesofobjectslook,determinewhetherornotyoursunglassesarepolarized.(Orifyoudon’thavesunglasses,findafriendwhodoes.)Clearlyexplainyourprocedure,observations,andanalysis.

DoThis:UsethePre-Lablinkonthelabwebsitetowatchanintroductiontothescienceofpolarizationinthecontextof3Dmovies.Youwillanswerseveralquestionsrelatedtothevideo.

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PL3.Howdopolarizedglassesmakesureeacheyeonlyseestheimageintendedforit,effectivelydoingthesamethingasclosingoneeye,withoutallthesquinting?

ReadThis:Modern3Dmoviesareprojectedusingcircularlypolarizedlight.However,thereisnofundamentalreasonwhy3Dmoviescouldn’tuselinearpolarization–theprojectorswouldjustneedtoproduceverticallyandhorizontallypolarizedlightandyouwouldwearthecorrespondingglasses.However,thereisonemajorpracticalissue.

PL4.Considera3Dmovieprojectedusinglinearlypolarizedlight.Whatwouldhappentothemovieifyouweretotiltyourheadwhilewearinglinearlypolarizedglasses?Explaintheproblemandwhycircularlypolarizedlightisasolution.

ReadThis:Nowyourbrotherishooked(anotherfishpun!)andwantstoknowmoreaboutwherepolarizationisused.Sunglassesand3Dmoviesaretwoofthemostcommonmodernusesofpolarization,buttherearemanymoreoutthere.Polarizationcanbeausefultool,evenwithoutunderstandingthescienceofwhat’shappening.Thisistrueforpeople(polarizationwasn’tdiscovereduntil1809–seeAppendixDfortheinterestingtale),plants,andanimals.

PL5.Doabitofindependentresearchtofindanexampleofhowpolarizationisused(notsimplywhereitexists:whereitisused),eitherinnatureorbypeoplepre-1809.Describethephenomenoninafewsentences,justlikeyouwouldtoalittlebrother.

ReadThis:InthefamousDoubleSlitExperiment,whichdemonstratesthedualnatureoflight,aslidethathastwoslitswithparticulardimensionshasbeenused.Theslidethatyouwilluseinthelabissimilartothat.Itcontainsfourdoubleslitconfigurationsofdifferentseparations.Youhavetopickoneofthem.But,whichoneisthebestfortheexperiment?

DoThis:OpentheDoubleSlitSimulationinIn-LabLinks.Therearethreeslidersbelowthesimulation.Thefirstoneiscalled“SlitWidth,”thesecond“Distancebetweenslits,”andthethirdone“Distancetothescreen.”Therearealsotabsfordifferentcolorsoflightandtypeofopenings.Spendsometimetoplaywithsimulationandfamiliarizeyourselfwiththediffractionpatterncreatedonthescreenandeachoftheslidersandtabs.

DoThis:ClickonSingleSlitandselecttheslitwidthtobe10micrometers.Then,changethedistancetothescreenbymovingthesliderleftandright.Observewhatwillhappenwiththediffractionpattern,particularlywiththewidthofthemaximumspot(thespotwherethelightintensityismaximum.)

PL6:Whathappenstothewidthofthemaximumwhenthedistancetothescreenchanges,butthewidthoftheslitiskeptconstant?

DoThis:ContinueusingtheSingleSlit,butatthistimekeepthedistancetothescreenconstantat1.5mandchangetheslitwidth.

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PL7:Whathappenstothewidthofthemaximumwhentheslitwidthchanges,butthedistancetothescreeniskeptconstant?

DoThis:Nowclickon“DoubleSlit”tab.Thesingleslitpatternbecomesanenvelopethatdefinestheintensitydistributionforthedoubleslit.Playwiththesliderswhileobservingthechangesofthemaximaonthescreen.

DoThis:Keeptheslitwidthconstantat12micrometersandthedistancetothescreenatthemaximumvalue,2meters.Changethedistancebetweentheslits.

PL8:Whathappenedtotheamountofthemaximainsidethe“envelope”?

DoNow:SynthesisQuestion1includesananalysisofthewavelengthuncertainty.ReadcarefullyCheckpoints1.4-1.7.AfteryoueliminatethesmallvaluesoffractionaluncertaintiesofdifferentvariablesinEq.1,youareleftwithonetermthatisthelargest.Sinceitisafractionalterm,thenominatorandthedenominatorofthefractionplaydifferentrolesinthevalueofthefraction.Playnowwiththesimulation.UsetheDoubleSlittabandhavethedistancetothescreenconstant.Changethedistancebetweentwoslits.

PL9:Inwhatscenarioistheuncertaintyofthewavelengthsmaller?

ReadThis:Justlikevisiblelight,x-rayscanbepolarized.ProfessorsKrawczynskiandBeilickearecollaboratorsinX-Caliber,anexperimentlookingatthepolarizationofx-raysemittedfromvariousexoticsources.Checkoutthelabwebsiteforlinkstodetails.

EndofPre-Lab

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PartI:TheDigitalRevolution

TheStory

YouarehomeforSpringBreakandyourtechnologically-challengedgrandparentsaretryingtoputoneofthosenew-fangledDVDsintotheiroldCDplayer.AfteryouintroducethemtotheDVDplayer,theyaskyouwhythehecktherehavetobesomanytypesofdiscsoutthere?!Whatistheadvantageofoneoveranother?YourgrandparentsmaynotknowaboutTwitterandiPods,buttheydoremembertheircollegephysics.YoudecidetobegintheirenlightenmentonthemyriadofadvantagesBlu-rayandDVDdiscshaveoverCDsbyexaminingtheamountofdataeachdisccanhold.Fortuitouslylyingaroundtheirhouseistheequipmenttobuildaninterferenceexperiment(theyreallyenjoyedcollegephysicslabs!).

Equipment

• Laserapparatuswithtwotestleads• Powersupply• Screen(rulermountedonringstand)• Slideofdoubleslitsinholder

• CD(labelremoved,cleardisc)• DVD(labelremoved,purplishtint)• Transparentvinylrecord• MeasuringTape

TheBasics

Thefirstthingyoudoisexplainthebasicsaboutcompactdiscs(CDs),digitalversatilediscs(alsocalleddigitalvideodiscs,orDVDs),andBlu-raydiscs.Allthreediscsaremadethroughsimilarprocesses.Thediscsaremadeofpolycarbonate(atypeofplastic),whicharethencoatedinaluminumandasmoothlayerofacrylic,andfinallycoveredbyalabel.Dataareetchedontothebottomsurfaceofthepolycarbonatebyalaserthatcreatesaseriesofbumpsofequalheight,butvaryinglength(Figure1).ThelaserinyourhomeCD/DVD/Blu-rayplayerreflectsoffthebumpsonthediscasitspinsandtheelectronicsinyourCD/DVD/Blu-rayplayerthenreadthisreflectedlightandtranslateitintoamovieorasong.Thedetailsofexactlyhowthishappensarecomplicatedandwellbeyondthescopeofyourexplanation.Fromthetopofthedisc(thelabelside),thesebumpsappeartobepits,whichiswhatpeoplecommonlycallthem.ForaCD,thepitsare500nmwide,125nmhigh,andaminimumof830nmlong.ThepitsonaDVDare320nmwide,120nmhigh,andaminimumof400nmlong.ThepitsonBlu-raydiscsareevensmaller.DVDsandBlu-raydiscscanhaveasecondpolycarbonatelayerthatalsostoresdata;thisishowdual-layerDVDsandBlu-raysarecreated.

Figure1:LayersofaDVD(drawingisnottoscale)

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Thepitsarelaidoutonthediscinaspiralpatternthatstartsatthecenterofthediscandcurvesoutwardtowardtheedge.Thespiralisetchedastightlyaspossible,andthedistancebetweenadjacentrings,knownasthe“trackpitch”(seeFigure2),dependsuponanumberofvariablesandisdifferentforeachtypeofdisc.

AninterestingbutnotterriblygermanepointinthisdiscussionofpitsanddiscsisthatscientistsatNorthwesternUniversityrecentlyusedthepitpatternsfromBlu-raymoviestoimprintsolarcells.Itturnsoutthatthepitshelpsolarcellsabsorbandstoremorelight,justlikepitshelpdiscsstoredata.Asithappens,anymoviewilldo,soMutantZombiePiranhasfromOuterSpacein3DworksjustaswellasCitizenKane.Formoreinformation,checkouttheIn-LabLinks.

TheadjacentringsinthetightspiralcanfunctionliketheslitsinYoung’sexperiment.Anyarrangementwithaverylargenumberofslitsisreferredtoasadiffractiongrating.Adiffractiongratingcanseparatewhitelightintoindividualwavelengths.Thisiswhydiffractiongratings,CDs,DVDs,andBlu-raydiscsallappeartohavearainbowofcolorontheirsurface.Withthisknowledgeinhand,youarereadytoprovetoyourgrandparentsthattheycanditchallthosebulkyCDsandputBarryManilow’sentirerepertoireononeconvenientdisc.

1.PreliminaryMeasurements-DeterminingtheWavelengthofaLaser

Yourealizethatwhileyourgrandparentsconvenientlyhavealasersetuponthediningroomtable,theydon’tknowitswavelength.“Butthelaserisred!”yourgrandparentsprotest,eagertogettothedatastorageexperimentalpunchline.Youpolitelyremindthemthat“red”isnotawavelength;“red”lightincludestherangeofwavelengthsfromabout620–700nm.YourealizethatbeforeyoucanlearnanythingaboutthetrackpitchofaCDorDVD,youwillneedtofindthewavelengthusingaslitofknownspacing.Beingsafetyconscious,youissuethefollowingwarningtoanyonewithineyeshotofalaser.

NWarning:Thelow-powerlaserbeamusedintheseexperimentswillnotcausepermanentdamagetoyourretina,butitcanproduceannoyingafter-imagesthatmaypersistforseveralminutesorlonger.DONOTallowthebeamtoshine(eitherdirectlyorbybouncingoffashinysurface)intoanyone’seyes.

Figure2:DataareetchedbyalaserinaspiralpatternontheCD,DVD,orBlu-raydisc.Thespacingbetweenadjacentringsinthespiralcorrespondstotheslitseparation(𝒅)inFigure5inAppendixB.Thisspacing,calledthetrackpitch,isaconstantforeachdisctype(drawingisnottoscale).

STOP

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DoThis:RemovetheCDandDVDfromthelaserapparatus.Youwon’tuseeitherofthemuntilSection2,buttheywilldisruptthefirstexperimentifyouleavethemon.(Figure3)

DoThis:Here’showtooperatethelaser.First,makesurethatthelaserisNOTconnectedtothepowersupply.Thenturnonthepowersupply.Setthevoltageto3.0V.Thelasercanbedamagedbygreatervoltages.Thelasercanalsobedamagedifyouconnectittothepowersupplybackwards.Keepingthatinmind,connectthelasertothepowersupplysuchthattheredterminalofthelaserisconnectedtotheredterminalofthepowersupply.Thatleavestheblackterminalofthelasertobeconnectedtotheblack(blue)terminalofthepowersupply.AlertyourLAIifthelaserdoesn’twork.

Checkpoint1.1:Takealookattheslide.Itcontainsfourdoubleslitconfigurationsofdifferentseparations.RefertoAppendixAforthedimensionsoftheconfigurations.Someoftheactuallabelsontheslidemighthavefallenorplacedinthewrongspotfromtheprevioususers.Whichconfigurationwillbemostusefultofindthewavelengthofthelaser?Recallthesimulationyouusedinthepre-lab.

DoThis:UsetheslitconfigurationyoudecidedoninCheckpoint1.1toproduceaninterferencepattern.YoucanreadmoreaboutitinAppendixB.Useanotebookoralooseleafpapertoseethepatern.Placethenotebookclosetotheslide.Whatdoyousee?Startslidingthenotebookawayfromtheslideandobservewhathappenstotheinterferencepattern.Atwhatpositiondoyouseethepatternmostclearly,closetotheslideorfarfromit?Usetherulermountedonastandorthepapermeasuringtape(youcantapeitonthewall)tomakethenecessarymeasurements.Pleasedonotmakeanymarksontheruleroronthewall.

Checkpoint1.2:Recordthedistancebetweentheslideandthescreen(𝐷)andthelocation(𝑦)ofthefirstordermaximum(𝑛 = 1).AdiagramoftheexperimentalsetupthathelpsdefinethevariablesisincludedinAppendixB.Thenuseyourmeasurementstocalculatethewavelengthofthelaser.

Checkpoint1.3:Nowrecordthelocation(𝑦)ofthemaximumwiththehighestorder(𝑛)thatyoucanclearlyidentify.(By“clearlyidentify”wemeanyouhaveabsolutelynodoubtaboutthevalueof𝑛towhichthemaximumcorresponds.)Don’tforgettorecordthevaluefor𝑛, aswell.Thenuseyourmeasurementstocalculatethewavelengthofthelaser.

Checkpoint1.4:EstimatetheuncertaintyinthedistancesthatyourecordedinCheckpoint1.2andCheckpoint1.3.Behonestwithyourselfhere!Evenifyouhadaninfinitelypreciseruler,

RemovetheCDandDVD

Figure3:RemovetheCDandtheDVDbeforedoingtheexperiment.

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thereisstilluncertaintyassociatedwithidentifyingthecenterofamaximum.Itisnotnearlyaswell-definedassomethingliketheedgeofatable.Sohowconfidentareyoureally?

ReadThis:Knowingtheuncertaintyinthosedistancesisnice,butwhatwe’dreallyliketoknowistheuncertaintyinthewavelengththatyoucalculated.Sincethewavelengthiscalculatedusingthevalues𝑛,𝑑,𝑦,and𝐷,theuncertaintyinthewavelengthwillbeafunctionofthosevaluesandtheiruncertainties.Itcanbeshown(AppendixE)thatforsmallanglesliketheonesyouaredealingwith,theuncertaintyinthewavelength,∆𝜆,isapproximatelygivenby

∆𝜆 = 𝜆 !!!

!+ !!

!

!+ !!

!

!+ !!

!

!

where𝜆isthebestguessvaluethatyouhavecalculated.InthenextfewCheckpointsyouwillsimplifythisequationandthenuseittoassessyourexperimentalwavelengthvalues.

Checkpoint1.5:Whatistheuncertaintyin𝑛?(Keepinmindthephrase“absolutelynodoubt”fromCheckpoint1.3.)RewriteEq.1takingthisintoaccount.

Checkpoint1.6:Theslideisaprecisionpieceoflabequipment,especiallywhencomparedtoameterstick.Theuncertaintyintheslitseparation(∆𝑑)issmallenoughforustoignore.SimplifytheequationyoucameupwithinCheckpoint1.5byignoringanyuncertaintycontributedbytheslide.

Checkpoint1.7:TheequationthatyouwrotedowninCheckpoint1.6isstillunnecessarilycomplicated.Asoftenhappens,oneofthesourcesofuncertainty(thatis,oneofthetermsundertheradical)ismuchlargerthantheotherterms.Discusswhichtermis,byfar,thelargest.Thenignorethesmallertermandsimplifytheexpressionfortheuncertaintyinthewavelength.

Checkpoint1.8:UsingtheequationyoufoundinCheckpoint1.7,writethewavelengththatyoufoundinCheckpoint1.2usingtheform𝜆 ± ∆𝜆.

Checkpoint1.9:UsingtheequationyoufoundinCheckpoint1.7,writethewavelengththatyoufoundinCheckpoint1.3usingtheform𝜆 ± ∆𝜆.

Checkpoint1.10:Discussyourtwovaluesforthewavelengthofthelaser.Addresseachofthefollowing:

a)Whichbestguessvaluedoyoutrustmore?Why?b)Arethetwovaluesconsistentwitheachother?Oristhediscrepancysignificant?c)Arethetwovaluesred?

ReadThis:Thisexerciseinuncertaintyanalysisreallyhighlightstheconceptsofabsoluteuncertaintyvs.fractionaluncertainty.Theabsoluteuncertaintyin𝑦issimply∆𝑦.Mostoftenthe

word“absolute”isleftout.Thefractionaluncertaintyin𝑦isdefinedas∆!!.Sometimesthisis

reportedasapercentage.

Eq.1

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ReadThis:Youshouldhavefoundthatthewavelengthyoucalculatedusingthelarger𝑦valuehadasmalleruncertaintythanthewavelengththatyoucalculatedusingthesmaller𝑦value.

Bothofthose𝑦valueshavethesameabsoluteuncertaintysincetheyweredirectlymeasuredinthesameway.However,thelarger𝑦valuehadasmallerfractionaluncertainty.Byreducingthefractionaluncertaintyofalengththatyouusedtocalculate𝜆,youwereabletogetamoreprecisevaluefor𝜆.Inmostcases,ifameasuredvaluehasahighfractionaluncertaintythenanythingyoucalculateusingthatmeasuredvaluewillhavealargefractionaluncertaintyaswell.

Checkpoint1.11:Showthatyouunderstandthedefinitionoffractionaluncertaintybycalculatingthefractionaluncertaintyforthe𝑦valuesyourecordedinCheckpoint1.2andCheckpoint1.3.Thencomparethesevaluestothefractionaluncertaintyinthevalueyourecordedfor𝐷anddiscuss.

SynthesisQuestion1(30Points):Youhavebeendirectedtoperformtwoexperimentstodeterminethewavelengthofthelaser.Sortthroughyournotesandwriteareportabouttheexperimentthatgaveyouthebetterresults.Acompleteresponsewillincludethefollowing:

• Diagramoftheexperimentalsetupthathelpsdefinethevariablesinequationsthatyouuse(Youmayrefertothisdiagraminyourotherresponsesaswell.)

• Anannotatedvisualization(sketch,plot,photo,etc.)oftheinterferencepatternthatshowswhatdistancesyoumeasured

• Calculationsofthewavelengthusingn=1andahigherorderofn• Calculationoftheuncertaintyinthewavelength.StartwithEq.1andshowhowyouuse

it.• Discussionaboutwhatstep(s)youtooktominimizetheuncertaintyinthewavelength

(otherthanrepeatedmeasurements)• Plausibilitystatementregardingyourresults

2.DeterminingTrackPitchoftheCD

Younowhaveallthetoolsinplacetodeterminethetrackpitchofthethreediscsthatyouhavebeengiven.

DoThis:ReplacetheslideofslitswiththeCD(theclearone)anduseitasadiffractiongratingtoproduceaninterferencepatternonthescreen.Notethatdespitehavingmanymoreslits,thediffractiongratingwillproducemaximainthesamelocationaspredictedbyYoung’stwoslitexperiment.SeeAppendixBforanexplanationofwhy.

ReadThis:Pleasebeawarethatscratchesonthediskcanproduceinterferencepatternsthatmightconfuseyou.TobecertainthatyouarelookingataninterferencepatterncreatedbythetrackintheCD,youshouldwatchthepatternasyouslowlyspinthedisk.Youtrackproducesaninterferencepatternthatchangesverylittleasyouspinthedisk.Ifyoufindaresultforthetrack

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pitchoftheCDthatisordersofmagnitudeoffofwhatyouexpect,thereisachancethatyouhavebeenlookingatapatternproducedbyascratchratherthanthetrack.

Checkpoint2.1:Measureallimportantdistancesandrecordtheminyournotes.

ReadThis:Recallthatthetrackpitch(ortrack

spacing)ofadiscreferstothespacingbetween

adjacentgroovesonthespiralthatholdsthe

information.PleaseseeFigure2orFigure4for

clarification.

Checkpoint2.2:Useyourdatatocalculatethetrackpitch(𝑑)oftheCD.

Checkpoint2.3:Whichordermaximumdidyouusetocalculatethetrackpitch?Explainwhyyouchoseoneorderoveranother.

Checkpoint2.4:Dosomemathtoshowwhyyoucouldn’tfindan𝑛 = 3maximum.

Checkpoint2.5:SearchonlinetofindaquotedvalueforthetrackpitchofaCD.Pleaserecordyoursourceinadditiontothevalue.

Checkpoint2.6:Figure7inAppendixCshowsaCDimagedbyascanningelectronmicroscope(SEM).UsethefiguretodeterminethetrackpitchofaCD.

SynthesisQuestion2(40Points):SortthroughyournotesandwriteareportshowinghowyoudeterminedthetrackpitchoftheCDandhowyouassessedtheplausibilityofyourresult.Acompleteresponsewillincludethefollowing:

• Anannotatedvisualization(sketch,plot,photo,etc.)oftheinterferencepatternthatshowswhatdistancesyoumeasured

• CalculationofthetrackpitchoftheCD• Mathshowingthatn=3maximumcannotbefound• Quantitativecomparison(%error)betweenyourexperimentalvalueandavaluefound

onlineandadiscussionbasedonthevalueofthe%error.Istheexperimentalvalueacceptable?

• TrackpitchfromFigure7inAppendixC.IncludeanannotatedpictureandanexplanationofhowthefigureisusedtomeasurethetrackpitchoftheCD.

• Quantitativecomparison(%difference)betweenyourexperimentalvalueandavaluefoundusingFigure7inAppendixCandadiscussionbasedonthevalueofthe%difference.

• Plausibilityoftheresult

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Figure4:Thespacingbetweenadjacentringsinthespiralcorrespondstotheslitseparation(𝒅)inFigure6inAppendixB.Thisspacing,calledthetrackspacingorthetrackpitch,isaconstantforeachdisctype(drawingisnottoscale).

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3.DeterminingTrackPitchofSomethingElse

ForthefinalSynthesisQuestion,youwilldeterminethetrackpitchofthepurplishDVD.

SynthesisQuestion3(30Points):PerformanexperimenttodeterminethetrackpitchthepurplishDVD.Youranswershouldcontainthefollowing:

• Anannotatedvisualization(sketch,plot,photo,etc.)oftheinterferencepatternthatshowswhatdistancesyoumeasured

• CalculationofthetrackpitchoftheDVD• Quantitativecomparison(%difference)betweenyourexperimentalvalueandavalue

youfoundusingFigure8inAppendixC.Includeanannotatedpictureandanexplanationofhowthefigureisusedtomeasurethetrackpitch.Discusswhethertheexperimentalvalueisacceptable.

• ComparisonbetweenthistrackpitchandthetrackpitchoftheCDalongwithaplausibilitystatementregardingthecomparison

• Explainhowtheinterferencepatternwouldchangeifyouusedabluelaserinsteadoftheredlaser

ReadThis:Hopefullyyourexperimentshaveshownthattakingaverycloselookatinterferencepatternscangiveyouverypreciseinformationaboutthegeometryofamaterial.Infact,scientistsusethesamebasicideasthatyouhaveusedinthislabtoanalyzecrystalstructures,examinewelds,andeventrytoimprovetheinternationalstandardforthekilogram!(YoumightwanttotakeasecondlookattheScientificAmericanarticleyoureadaspartofthePre-LabtotheMeasurementlablastsemester.)TheLaboratoryforMaterialsPhysicsResearchatWashUuseselectrondiffraction,x-raydiffraction,andneutrondiffractiontostudythestructureofvarioussubstances.Seethelabwebsiteforlinkstodetails.

TimetoCleanUp!

PleasecleanupyourstationaccordingtotheCleanup!Slideshowfoundonthelabwebsite.

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AppendixA:DoubleSlitSlide

Allfourconfigurationsaredoubleslits,buttheseparationbetweenthetwoslitsdiffersforeachpattern.Use the center-to-center slit separation (printedbeloweachpattern, inmm)as thequantity𝑑 in theformulainAppendixB.Eachindividualslitis0.15mmwide.

Ourslitsareveryexotic,importedallthewayfromGermany(GutenTag!).Thismeansthatthenumbersarewritten in the European style, so commas are used in place ofwhat you are used to seeing as adecimalplace.Therefore,thefirstpairofslitshasaseparationof0.25mm,etc.

Figure5:Slidecontainingfourdoubleslitpatterns

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AppendixB:InterferenceandDiffraction

Huygens’sPrinciplestatesthatgivenawavefrontatsomeinitialtime,subsequentwavefrontscanbeconstructedatsomelatertimebytreatingeachpointontheinitialwavefrontasthesourceofacircularwavethatspreadsoutwithafixedamplitudeandspeed.Diffractionoccurswhenawavebendsaroundanobstacleitencounters,suchasaslit,andsubsequentlyspreadsoutintoacircularwaveaccordingtoHuygen’sPrinciple.Thiswillcreatepointsofconstructiveanddestructiveinterference,resultinginadiffractionpattern.

Whentherearemultipleslits,eachwavenotonlyconstructivelyanddestructivelyinterfereswithitself,asindiffraction,butalsowiththewavefrontsfromtheotherslits.Theresultingsequenceofbrightanddarkspotsiscalledaninterferencepattern.Thisistrueforalltypesofwaves,includingsound,water,andlightwaves.

ThelocationPofthe𝑛thpointofconstructiveinterferenceisgovernedbythefollowingequation:

𝑑 sin 𝜃 = 𝑛𝜆

ThelocationPofthe𝑛thmaxima,asmeasuredfromthecentralaxisisgivenbythefollowingequation:

𝑦 = 𝐷tan 𝜃

Where:𝑛isanintegerdescribingthemaximaofinterest,locatedonascreenatpointP;𝜃istheanglebetweenthecentralaxis(𝑛 = 0)andP;𝑦 isthedistancebetweenthecentralaxisandP;𝐷isthedistancebetweentheslitandthescreen;𝜆isthewavelengthoflight;and𝑑isthecenter-to-centerdistancebetweentheslits(Figure6).

Figure6:Young’sdoubleslitexperiment

Diffractiongratings,liketheonesusedinthislab,canhavemanyslits,allwiththesameseparation𝑑.YouhavetoaddintheextrawavesatPfromeachoftheseextraslits,takingproperaccountoftheirphaseshifts.Eachnewslitwilladdinawaveshiftedinphasebyδfromtheonebefore.Thismakesforsignificantlymorecomplicatedinteractions.However,theconditionforconstructiveinterferenceofthelightfromalltheslitsisunchanged–theinterferencemaximaremainatthesameanglesasinthecase

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oftwoslits.Themaindifferenceisthatthemaximabecomenarrowerandnarrowerasthenumberofslitsincreases.

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AppendixC:Close-upsoftheDiscs

ThisappendixcontainstwoimagescreatedusingaScanningElectronMicroscopeorSEM.AlloftheSEMimageswereproducedbyChrisSupranowitzattheUniversityofRochesterandcanbefoundonhiswebsite:http://www.optics.rochester.edu/workgroups/cml/opt307/spr05/chris/

Figure7:SEMimageofaCD.Thelighterfeaturesarepits.Notethescale.

Figure8:SEMimageofaDVD.Thelighterfeaturesarepits.Notethescale.

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AppendixD:PolarizationandMalus’Law

ABitofHistory

In1808,physicistEtienne-LouisMaluswasgazingthroughapieceofIcelandicspar,averycleartypeofcalcite crystal, at the sunset reflecting off thewindows of the Luxemburg Palace in Paris. He noticedsomeverystrangethingshappeningwhenherotatedthecrystal,apropertythatwouldeventuallybeunderstoodasdoublerefraction(sometimescalleddoublediffractioninstead).Malus’observationsonthat evening prompted him to explore the phenomenon further, leading to the first scientificexplanation of polarization. For his troubles,Malus received the very nifty honor of being one of 72French scientists, engineers, and mathematicians to have their names inscribed on the Eiffel tower(othernamesyoumightrecognizefromthissemesterareAmpère,Fourier,andCoulomb).

Malus’Law

Atitsmostbasiclevel,Malus’Lawmathematicallydescribeshowpolarizersaffectthelightthatpassesthroughthem.Whenunpolarizedlightpassesthroughapolarizer,onlycomponentsoftheelectricfieldvectorparalleltotheaxisofpolarizationwillgetthrough.Thisistrueforeachpolarizer,whetherthereisone,two,ortwenty.

Let’staketherelativelysimplecaseoftwopolarizers.Ifwewanttoknowhowmuchlightfromthefirstpolarizerwillmake it through the second,we can just look atwhat’s going onwith the electric fieldvectors.AsFigure9shows,onlycomponentsoftheelectricfieldparalleltotheaxisofpolarization(andtherefore parallel to𝐸! – see Figure 9) will be able to pass through the second polarizer. However,rememberthattheelectricfieldthatalreadypassedthroughthefirstpolarizer(𝐸!)andisnowincidenton the second polarizer is composed of two component vectors: one parallel to 𝐸! and oneperpendicularto𝐸!.Thesecomponentsarelabeled𝐸║and𝐸┴ ,respectively,inFigure9.

Figure9:Componentsoftheelectricfieldthatwillpassthroughpolarizersorientedatanangle𝜃withrespecttooneanother.

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Therefore,thefractionoftheelectricfield(𝐸)thatpassesthroughboththefirstandsecondpolarizerisequalto:

𝐸 = 𝐸! cos 𝜃

Sincethe intensityof light isproportionaltothesquareoftheelectricfield,thetotal intensityof lightthat(𝐼)thatpassesthroughboththefirstandsecondpolarizerisequalto:

𝐼 = 𝐸!! cos! 𝜃 = 𝐼! cos! 𝜃

Finally, if we generalize this equation so that the light that passes through the first polarizer and isincidentonthesecondpolarizerhasthesubscript𝑖wehaveMalus’Law:

𝐼 = 𝐼! cos! 𝜃

Inthecaseofmorethantwopolarizers,Malus’Lawcanbeusedforeachsetofpolarizers. Justapplythe law separately to each pair of polarizers! For the case of three polarizers in a row, you wouldtherefore need to apply Malus’ law to the first and middle polarizer together and determine theintensityof light thatemerges from themiddlepolarizer. ThenapplyMalus’ lawagainwith the lightthatemergedfromthemiddlepolarizerastheincidentlightonthethirdpolarizer.