Zeeman effect with an electromagnet and a CCD camera

Student'sSheet

Printed:11.08.201712:42:20|P2511005

Robert-Bosch-Breite10 Tel:+49551604-0 [email protected]

D-37079Göttingen Fax:+49551604-107 www.phywe.com

Difficulty

Difficult

PreparationTime

1Hour

ExecutionTime

2Hours

RecommendedGroupSize

2Students

ZeemaneffectwithanelectromagnetandaCCD

camera(ItemNo.:P2511005)

CurricularRelevance

AdditionalRequirements: ExperimentVariations:

Keywords:

Bohr’satomicmodel,quantisationofenergylevels,electronspin,Bohr’smagneton,interferenceofelectromagneticwaves,Fabry-Perot

interferometer

Overview

Shortdescription

Principle

The“Zeemaneffect”isthesplittingupofthespectrallinesofatomswithinamagneticfield.Thesimplestisthesplittingupof

onespectrallineintothreecomponentscalledthe“normalZeemaneffect”.ThenormalZeemaneffectisstudiedusingacadmi

mspectrallampasaspecimen.Thecadmiumlampissubmittedtodifferentmagneticfluxdensitiesandthesplittingupofthe

redcadmiumline(643.8nm)isinvestigatedusingaFabry-Perotinterferometer.Theevaluationoftheresultsleadstoafairly

precisevalueforBohr’smagneton.

Fig.1:ExperimentalsetupwithCCD-camera.

AreaofExpertise:

Physics

EducationLevel:

University

Topic:

ModernPhysics

Subtopic:

QuantumPhysics

Experiment:

Zeemaneffectwith

anelectromagnetand

aCCDcamera

Student'sSheet

Printed:11.08.201712:42:20|P2511005



Equipment

PositionNo. Material OrderNo. Quantity

1 Fabry-Perotinterferometer 09050-03 1

2 Electromagnetw/opoleshoes 06480-01 1

3 CadmiumlampforZeemaneffect 09050-20 1

4 PHYWEvariabletransformerDC:0...20V,12A/AC:0...25V,12A 13531-93 1

5 Powersupplyforspectrallamps 13662-97 1

6 Rotarytableforheavyloads 02077-00 1

7 Polepieces,drilled,conical 06480-03 1

8 Polarizationspecimen,mica 08664-00 1

9 Opticalbenchexpert,l=1000mm 08282-00 1

10 MOTICMoticam1CMOSTechnology 63300-00 1

11 Capacitor,electrolyt.,22000µF 06211-00 1

12 Diaphragmholder 08040-00 1

13 Polarisingfilter,onstem 08610-00 1

14 Irisdiaphragm 08045-00 1

15 HolderforMoticamonopticalbenchandopticalbaseplate 63300-01 1

16 DMMwithNiCr-Nithermocouple 07122-00 1

17 Slidemountforopticalbenchexpert,h=80mm 08286-02 2

18 Slidemountforopticalbenchexpert,h=30mm 08286-01 6

19 Baseforopticalbenchexpert,adjustable 08284-00 2

20 Lensholder 08012-00 4

21 Lens,mounted,f+300mm 08023-01 1

22 Lens,mounted,f+50mm 08020-01 2

23 Connectingcord,32A,1000mm,red 07363-01 1

24 Connectingcord,32A,1000mm,blue 07363-04 1






Tasks

1. UsingtheFabry-Perotinterferometer,aself-madetelescope,aCCD-cameraandmeasurementsoftware,thesplittingupof

thecentrallineintotwo -linesismeasuredinwavenumbersasafunctionofthemagneticfluxdensity.Intheclassical

versionwheretheCCD-Cameraisnotavailable,ascreenwithscaleandaslidingdeviceareusedtomeasurethesplitting.

2. Fromtheresultsofpoint1.avalueforBohr'smagnetonisevaluated.

3. Thelightemittedwithinthedirectionofthemagneticfieldisqualitativelyinvestigated.

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Set-upandProcedure

Theelectromagnetisputontherotatingtableforheavyloadsandmountedwiththetwopole-shoeswithholesinsuchaway

thatagaplargeenoughfortheCd-lamp(9-11mm)remainsfortheCd-lamp.Thepole-shoeshavetobewelltightenedinsucha

waythattheycannotmovelateronwhenthemagneticfluxisestablished.TheCd-lampisinsertedintothegapwithout

touchingthepole-shoeandconnectedtothepowersupplyforspectrallamps.Thecoilsoftheelectromagnetareconnectedin

parallelandviaananmeterconnectedtothevariablepowersupplyofupto20VDC,12A.Acapacitorof22000μFisinparallel

tothepoweroutputtosmoothentheDC-voltage.Theopticalbenchforinvestigationofthelinesplittingcarriesthefollowing

elements(theirapproximatepositionincmisgiveninbrackets):

(80)CDC-Camera

(73)L3=+50mm

(45)Analyser

(39)L2=+300

(33)Fabry-PerotEtalon

(25)L1=+50mm

(20)Irisdiaphragm

(20)Drilledpole-shoes

(0)Cd-spectrallamponrotatingtable

Fig.2:Arrangementoftheopticalcomponents.

TheirisdiaphragmiseliminatedforinitialadjustmentandfortheobservationofthelongitudinalZeemaneffect.During

observationofthetransverseZeemaneffecttheirisdiaphragmisilluminatedbytheCd-lampandsuchitactsasthelight

source.Thelens andalensof ,incorporatedintheetalon,createanearlyparallellightbeamwhichtheFabry-

Perotetalonneedsforaproperinterferencepattern.Theetaloncontainsaremovablecolourfilterthatletstheredcadmiumline

at643.8nmpass.Thelens producesaninterferencepatternofringswhichcanbeobservedthrough .Therings

diameterscanbemeasuredusingtheCCD-cameraandthesoftwaresuppliedwithit.Intheclassicalversiontheinterference

patternisproducedwithintheplaneofthescreenwithascalemountedonaslidemountwhichcanlatterallybedisplacedwith

aprecisionof1/100thofamilimeter.Themeasurementherecanbedoneforinstance,bysystematicdisplacementoftheslash

representingthe„0“ofthescale.

Theinitialadjustmentisdoneinthefollowingway:

Therotatingtablewithelectromagnet,pole-shoesandCdlampalreadymountedisadjustedsothatthecenteroftheholesinthe

pole-shoesliesabout28cmabovethetable.Theopticalbenchwithallelements(exceptirisdiaphragmandCCD-camera)

mounted,isthenmovedclosertotheelectromagnetinsuchawaythatoneoftheoutletholesofthepoleshoescoincideswith

thepreviouspositionoftheirisdiaphragm.L1isthenadjustedsothattheoutletholeiswithinthefocalplaneofit.Allother

opticalelementsofFig.2.aresubsequentlyreadjustedwithrespecttotheirheightcorrespondingly.Thecurrentofthecoilsisset

forsometimeto8A(increaseinlightintensityoftheCd-lamp!)andtheringinterferencepatterninaxialdirectionisobserved

throughL3bytheeye.Thepatternmustbecenteredandsharpwhichiseventuallyachievedbyalast,slightmovementofthe

etalon(totherightortotheleft)andbydisplacementofL2(verticallyandhorizontally).FinallytheCCD-camerawiththe8mm

lensattachedismountedtotheopticalbenchandadjustedinhorizontalandverticalpositionaswellasintiltandfocusuntila

clearpictureoftheringpatternisvisibleonthecomputerscreen.Forinstallationanduseofthecameraandsoftwareplease

refertothemanualsuppliedwiththecamera.Hint:bestresultsareachievedwhentheexperimentiscarriedoutinadarkened

room.Theelectromagnetisnowturnedby90°,theirisdiaphragmisinsertedandtheanalyzerturneduntiltheπ-line

(explanationfollows)disappearscompletelyandthetwos-linesappearclearlyvisible.

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Remark:

Forlaterevaluationsthecalibrationcurveofthemagneticfluxdensityversusthecoilcurrenthastobetracedpreviously.This

canbedoneifateslameterisavailable.OtherwisetheresultsofFig.3mustbeused.ThecurveofFig.3wastracedby

measuringthefluxdensityinthecenterofthegapintheabsenceoftheCd-lamp.Fortheevaluationsthesecenter-valueswere

increasedby3.5%toaccountforthenon-uniformfluxdistributionwithinthegap.

Fig.3:MagneticfluxdensityBinthe

centreofthegapwithoutCd-lamp

(gapwidth:9mm)asafunctionofthe

coilcurrent.

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TheoryandEvaluation

Theory

Asearlyas1862,Faradayinvestigatedwhetherthespectrumofcolouredflameschangesundertheinfluenceofamagneticfield,butwithoutsuccess.Itwasnotuntil1885thatFievezfromBelgiumwasabletodemonstrateaneffect,butitwasforgottenandonlyrediscovered11yearslaterbytheDutchmanZeeman,whostudiedittogetherwithLorentz.HeretheeffectisdemonstratedwiththelightofaCadmiumlampandthehelpofaFabry-Perotinterferometerforresolvingasmallpartofthespectrumpreselectedbyacolorfilteroraninterferencefiltersoonlythelightofasingleatomictransitionlineisobserved.Withoutfieldthemagneticsub-levelshavethesameenergybutwithfieldthedegenerationofthelevelswithdifferentmJiscancelledandthelineissplit.Cadmiumhastheelectronstructure(Kr)4d105s2,i.e.theoutershelltakingpartinopticaltransitionsiscomposedbythetwo5s2electronsthatrepresentacompletedelectronshell.((Kr)=1s22s22p63s23p63d104s24p6.)ThisissimilartotheouterelectronstructureofHeliumbutalsoofMercury.AschemeoftheenergylevelsofCdisshowninFig.4.Inacompletedshellinit'sgroundstatetheelectronspinsalwayscompensateeachother–theyareanti-parallel.Ifthetotalelectronspiniszero,alsothemagneticmomentconnectedtoelectronspiniszero.Atomicstateswithzerototalspinarecalledsingulettstates.Sointransitionsbetweendifferentsingulettstatesthemagneticmomentofspindoesnotplayarole,asisthecasewiththenormalZeemaneffect.Electricdipoleradiationasincommonopticaltransitionsdoesnotchangetheelectronspinexceptinheavyatomswithjj-coupling,sotransitionsarenormallybetweendifferentstatesinthesamemultiplicitysystem.ButFig.4showsthereissomejj-couplinginCadmium.ThetransitionusedtodemonstratethenormalZeemaneffectis with643.847nmandthetransitionusedtodemonstratetheanomalousZeemaneffectis with508.588nm.Inatermlike thefirstnumber„2“denotesthemainquantumnumberoftheradiatingelectronwithrespecttotheatom's

groundstate(thatiscountedas„1“),herethisisreallythe6ths-shellsince isthegroundstate.(Thisiswhythe2P-states

arebelowthe2S–states, denotesthe5thp-shellsinceKryptonhas ).Theupper„3“denotesthemultiplicity,thatis2s+1withsherethespinquantumnumber.Thelower„1“denotesquantumnumberjofthetotalangularmomentum,i.e.

, ,…, withIthequantumnumberoftheangularmomentumoftheorbit.„S“,„P“,„D“,„F“denotetheactualvalueofI,i.e.„S“means ,„P“means ,…

isatransitionwithinthesingluettsystemsothespinmagneticmomentshavenoeffect.Butinthetransitiontriplettstatesareinvolvedandthespinmagneticmomentdoesnotvanishinallsub-states.

Theselectionruleforopticaltransitionsis andtheradiationbelongingtotransitionswith arecalled

-linesandtheoneswith arecalled -lines.Withthemagneticfieldturnedonintheabsenceoftheanalyser

threelinescanbeseensimultaneouslyinthenormalZeemaneffectintransversalobservation.InthecaseoftheanomalousZeemaneffectthreegroupsofthreelinesappear.InsertingtheanalyserinthenormalZeemaneffecttwo -linescanbeobservediftheanalyserisintheverticalposition,whileonlythe -lineappearsiftheanalyseristurnedintoitshorizontalposition(transversalZeemaneffect).IntheanomalousZeemaneffecttherearetwogroupsofthree -linesinverticalpolarization.Turningtheelectromagnetby90°thelightcomingfromthespectrallampparalleltothedirectionofthefield(longitudinal)canalsobestudiedthroughtheholesinthepolepieces.Itcanbeshownthatthislightiscircularpolarizedlight(longitudinalZeemaneffect).Fig.5summarizesthefacts.A -plateisgenerallyusedtoconvertlinearintoellipticalpolarized

light.Inthisexperimentthe -plateisusedintheoppositeway.Withthe -plateinsertedbeforetheanalyser,thelightof

thelongitudinalZeemaneffectisinvestigated.Iftheopticalaxisofthe -platecoincideswiththevertical,itisobservedthat

someringsdisappeariftheanalyserisatanangleof+45°withtheverticalwhileotherringsdisappearforapositionof-45°.ThatmeansthatthelightofthelongitudinalZeemaneffectispolarizedinacircular(opposedway).The -linesarelongitudinallynotobservable.




Fig.4:TheatomicstateofCadmium,wavelengthinA=0.1nm.

Fig.5:LongitudinalandtransversalZeemaneffect.

InthenormalZeemaneffectwiththetransition with643.847nmtheelectronspinscanceleachotherinboththeinitialandfinalstateandtheenergyofanatomicstateinamagneticfielddependsonlyonthemagneticmomentsoftheelectronorbit.Themagneticmomentoftheorbitalangularmomentumis

withBohr'smagneton

andthegyromagneticfactoroforbitalangularmomentum .

Inthevectormodeloftheatomtheenergyshiftscanbecalculated.Itisassumed,thatangularmomentsandmagneticmomentscanbehandledasvectors.Angularmomentandthemagneticmomentconnectedwithitareantiparallelbecauseofthenegativeelectroncharge.Theamountoftheorbitalmagneticmomentoftheorbitalangularmomentum,withquantumnumber suchthat




,is:

IncaseofLS-coupling(Russel-Saunderscoupling,spin-orbitcoupling)formanyelectronsystemsistheamountofthetotalangularmomentum

with

thesumofthespinsofthesingleelectronsand

thesumoftheorbitangularmomentsofthesingleelectrons.Hereitis

So

Theamountofthecomponentofthecorrespondingmagneticmoment indirectionof is:

with .

Observableisonlytheprojectionofthemagneticmomenton

withit'squantizationwithrespecttoz-axis

withthemagneticquantizationnumberwith Theinteractionenergywiththeoutermagneticfield alongthez-axisisthen

HeretheusedtransitionforthenormalZeemaneffectis .

Sointheinitialstateis , and . mayhavethevalues .Thegyromagneticfactorisandtheenergydifferencebetweentwoneighbouringsubstatesoftheinitialstateisthen .

Inthefinalstateis , and . mayhavethevalues .Thegyromagneticfactoris

andtheenergydifferencebetweentwoneighbouringsub-statesofthefinalstateisthen ,too,i.e.fortransitionwiththesame betweeninitialandfinalstatetheenergyshiftisforinitialandfinalstatethesame–sotheyhavealtogetherthesamefrequency.Fig.6showstheresultingtransitiondiagram.




Forelectricaldipoletransitionstheselectionrulestates .Theenergyshiftofatransitionbetweeninitialstatewith and isthen

andherethe( )-valuesaresimplyequalto .SoincaseofLS-couplinginthenormalZeemaneffectthree

equidisantlinesareexpectedinthistransitionwithadistanceinfrequencyorwavenumberproportionaltothemagneticfieldstrength.Thepolarizationofthetransitionswith intransversalobservationisparalleltothemagneticfield(herehorizontal)andoftheothertransitionsthepolarizationisperpendiculartothat.

Fig.6:Energyshiftoftheatomicstates.

TheanomalousZeemaneffectisthemoregeneralcasewheretheelectronspinsdonotcanceleachotherandtheenergyofanatomicstateinamagneticfielddependsonboththemagneticmomentsofelectronorbitandelectronspin.

Themagneticmomentoftheorbitalangularmomentum isasabove(see(*))andthemagneticmomentofthespin is

withthegyromagneticfactoroforbitalangularmomentum .

Additionaltotheorbitalmagneticmomentoftheorbitalangularmomentum theamountofthespinmagneticmomentofthespin ,withquantumnumber suchthat

hastobetakenintoaccount:

IncaseofLS-coupling(Russel-Saunderscoupling,spin-orbitcoupling)formanyelectronsystemstheamountofthetotalangularmomentumis

with

thesumofthespinsofthesingleelectronsand




thesumoftheorbitangularmomentsofthesingleelectrons.Inthevectormodelitisassumed,thatangularmomentsandbothspinandorbitalmagneticmomentscanbehandledasvectors.Sothecosineruleappliesforthesumoftwovectorswithan

anglebetweenthem.Theamountofthecomponentofthecorrespondingmagneticmoment indirectionof iswiththeapproximation :

with

Observableisonlytheprojectionofthemagneticmomenton

withit'squantizationwithrespecttoz-axis

withthemagneticquantizationnumber with Theinteractionenergywiththeoutermagneticfield alongthez-axisisthen

HerefortheanomalousZeemaneffecttheusedtransitionis .Sointheinitialstateis , and . mayhavevalues .The

gyromagneticfactoris

andtheenergydifferencebetweenneighbouringsub-statesoftheinitialstateisthen

Inthefinalstateis , and . mayhavethevalues .Thegyromagneticfactoris

andtheenergydifferencebetweenneighbouredsub-statesofthefinalstateisthen

Fig.7showstheresultingtransitiondiagram.




Fig.7:Energyshiftoftheatomicstates.

Forelectricaldipoletransitionstheselectionrulestates .Theenergyshiftofatransitionbetweeninitialstatewith and andfinalstatewith and isthen

Thefollowingtableshowstheenergyshiftsofthetransitions:

Fig.8:Reflectedandtransmittedraysattheparallelsurfaces(1)and(2)oftheétalon.Theétalonspacingis .

SoincaseofLS-couplingintheanomalousZeemaneffectnineequidistantlinesareexpectedinthistransitioninsteadofthreewithoutspinmagnetism.Thepolarizationofthetransitionswith intransversalobservationisparalleltothemagneticfield(herehorizontal)andthepolarizationoftheothertransitionsisperpendiculartothemagneticfield.Atobservingthe -linesofthetransversalZeemaneffectitiseasytoseethattheamountofsplittingincreaseswithincreasingmagneticfieldstrength.Foraquantitativemeasurementofthissplittingintermsofnumberofwavelengths,aFabry-Perotinterferometerisused,thefunctioningofwhichhastobeexplained:TheFabry-Perotétalonconsistsofaquartzglassplateof3mmthicknesscoatedonbothsideswithapartiallyreflectinglayer(90%reflection,10%transmission).Letusconsiderthetwopartiallytransmittingsurfaces(1)and(2)inFig.8seperatedbyadistance .AnincomingrayformingananglewiththeplatenormalwillbesplitintotheraysAB,CD,EF,etc.thepathdifferencebetweenthewavefrontsoftwoadjacentrays(e.g.ABandCD)is

whereBKisdefinednormaltoCDand istherefractiveindexofquartzat509nm, .At644nmis .With

and

weobtain




andforaconstructiveinterferenceitis:

(1)

where isanintegerand thelight'swavelength.Equation(1)isthebasicinterferometerequation.LettheparallelraysB,D,F,etc.bebroughttoafocusbytheuseofalensoffocallength asshowninFig.9.

Fig.9:FocusingofthelightemergingfromaFabry-Perotétalon.Lightenteringtheétalonatanangleθisfocusedontoaringofradiusr=fθwherefisthefocallengthofthelens.

For fulfillingequation(1)brightringswillappearinthefocalplanewiththeradius

(2)

forsmallvalues ,e.g.raysnearlyparalleltotheopticalaxis.Since

(3)

If correspondstoabrightfringe, isaninteger.Howeveris theinterferenceconditionforthecenter(for )generallynotaninteger.If istheinterferenceorderofthefirstring,itis since .Wethenlet

where istheclosestintegerto (smallerthan ).Ingeneralisforthepthringofthepattern,measuredstartingfromthecenter,thefollowingisvalid:

(4)

Combiningequation(4)withequations(2)and(3),weobtainfortheradiioftherings,writing for ,

(5)




Wenotethatthedifferencebetweenthesquaresoftheradiiofadjacentringsisaconstant:

(6)

canbedeterminedgraphicallyplotting versus andextrapolatingto .

Now,iftherearetwocomponentsofaspectralline(splittingofonecentrallineintotwocomponents)withwavelengthsand ,whichareveryclosetooneanother,theywillhavefractionalordersatthecenterand :

where and arethecorrespondingwavenumbersand , istheinterferenceorderofthefirstring.Hence,ifthe

ringsdonotoverlapbyawholeorderso andthedifferenceinwavenumbersbetweenthetwocomponentsis

(7)

Usingequations(5)and(6),weget

(8)

Applyingequation(8)tothecomponentsaandb,yields

and

Bysubstitutingthesefractionalordersintoequation(7),wegetforthedifferenceofthewavenumbers:

(9)

Fromequation(6)wegetthedifferencebetweenthesquaresoftheradiiofcomponenta:

thisisequalto(withinaverysmallpart)thesamedifferenceforcomponentb

Henceweassume




forallvaluesofp.Similarly,allvalues

mustbeequal,regardlessof (theorderofinterference)andtheiraveragemaybetakenasmaybedoneforthedifferent -values.With (thedifferenceofsquaresofradiiofdifferentlinesofthesameorderofinterference)and (differenceofsquaresofradiiofdifferentorders)asaveragevalueswegetforthedifferenceofthewavenumbersofthecomponentsaandb:

(10)

Fig.10:NormalZeemaneffect:Interferencepatternwithoutpolarisationfilterfornocoilcurrentandfor5Acoilcurrent.Ontheleftthereisoneringperorderofinterference,ontherighttherearethreeringsperorderofinterference.

Note:Equation(10)showsthatΔkdoesnotdependonthedimensionsusedinmeasuringtheradiioftheringsystem.

AnomalousZeemaneffect:Forallthesepicturesthecoilcurrentwassetsuchthatthedifferentordersofinterferencewerejuststillseparated.Thiswasthecasewith5Aonthemagnetcoils.InFig.11alltheringsarevisiblebuthardtocount.InFig.12themiddlethreeringsarevisiblewith .InFig.13theouterandinnerthreeringswith arevisible,that'ssix

ringsmakingatotalofninerings.Theringsseemtobeequidistantbutnotofthesameintensity.

Fig.11:AnomalousZeemaneffect:Interferencepatternwithoutpolarisationfilterandmagnifiedcut-outofthefirstcompletelyvisibletwoordersofinterference.




Fig.12:AnomalousZeemaneffect:Interferencepatternwithhorizontalpolarisationfilterandmagnifiedcut-outofthefirstcompletetwoorders.

Fig.13:AnomalousZeemaneffect:Interferencepatternwithverticalpolarisationfilterandmagnifiedcut-outofthefirstcompletetwoorders.

Evaluation

Theradiioftheringshavetobemeasuredatdifferentmagneticfluxdensities.Withequation(10)thecorrespondingdifferenceinwavenumbers isthendetermined.Weproceedintwosteps:Firstwetakepicturesoftheringpatternsatdifferentcoilcurrents/magneticfieldstrengths.Theninasecondsteptheringdiametersinthesepicturesaremeasured.Togetalifepicturefromthecameragotothe<File>menuandchoosetheentry<CaptureWindow>.Inthecapturewindowthesettingsregardinge.g.contrast,brightnessandsaturationoftheimagecanbeoptimisedviathemenuyougettowhenchoosing<VideoCaptureFilter>fromthe<Option>menu.Whensatisfiedwiththeimagequalityandacertaincoilcurrent(magneticfield)isestablished,thepictureiscapturedbychoosing<StillImage>fromthe<Capture>menu.Atthisstageitisadvisabletogotothemainwindowandwritethevalueofthecoilcurrentandthepolarizationatwhichthepicturewastakenintoitbyusingthe<Text>tool.Thispreventsamix-uplateron.

NormalZeemaneffect:

Theaboveprocedureisrepeatedusingdifferentmagneticfieldswithoutpolarizationfilterintransversalobservationforcoilcurrentssuchthattheobservedringpatternsofdifferentordersdonotoverlap.Oncethesepictureshavebeencollected,proceedtomeasuretheradiioftheringschoosing<Circle>fromthe<Measure>menu.Bymovingthemouseacrossthepicture,acircleisdrawn.Fitthiscircleinsizeandpositionasgoodaspossibletoaringofinterest.Youwillseethatradius,areaandperimeterofthecirclewillbedisplayedinalittleboxandinatablebelowthepicture(cf.Fig.14).Whatwearemainlyinterestedinisthesquareoftheradiusofthecircle–sowecanusetheareadata.Notethattheunits(μm,mm,cm)areofnoimportanceinthisexperiment,thatmeansnocalibrationofthecamerahastobeperformedandthefactor …canbeneglected.Allthevisibleringsmaybeevaluated,i.e.threeringsperorderofinterference,themiddleoneofthemwithunchangedwavelength.Proceedtodrawandfitcirclestoasmanyordersofringsasaresuitableinthepicture,thiswillgiveyou ; ; ;….Dothesamewiththeotherpicturescaptured.IntheclassicalversionwithouttheCCD-

cameraforeachfieldstrengthasetofradiiofringsisdeterminedinthefollowingway:Theslashofthescale„0“isshiftedhorizontallyalongadiameterthroughtheringpatternuntilitcoincidese.g.withtheouterringofthefourthordertotheleftintowhichthefourthringhassplit.Alwaysapproachfromthesameside,e.g.fromlefttoright,forcorrectreadings.Thefirstvalueisdenoted.The„0“slashisthenmovedfromlefttoright,thenextreadingtakenatthemiddleringofthe4thringsystem,thenextattheinnerringofthe4thringsystemandsoonuntiltheouterringontherightofthe4thringsystemisreached.Thelastreadingminusthefirstreadingdividedbytwothenprovidestheradius andsoon.Usingtheslidemount,allreadingsare

donein“mm“withaprecisionof1/100thofamm.InFig.15foragivenfieldstrengthdwascalculatedfromthedifferencesof




areasofcorrespondingringsofdifferentordernumberandsubsequentaveraging(e.g.differenceofareabetweenmiddleringofsecondorderandmiddleringoffirstorder)and wascalculatedfromthedifferencesofringareasofthethreeringsofthesameordernumber(outertomiddleandmiddletoinner)andsubsequentaveragingoverallvalues.With

so

With

fromtheregressionofthemeasuredvaluesand , , ,thisyields

Theliteraturevalueis .

Fig.14:Screenshotofsoftwareusedtomeasuretheradiiofinterferencerings,evaluationofhorizontalandverticalpolarisation.




Fig.15:Measurementresultsfor vs.magneticfieldstrength.

AnomalousZeemaneffect:

Theaboveprocedureisrepeatedwithouttheredcolourfilterandnowusingthegreeninterferencefilter.Capturepicturesfordifferentcoilcurrentstrengthsforeachhorizontalandverticalpolarizationintransversalobservationforcoilcurrentssuchthattheobservedringpatternsofdifferentordersdonotoverlapsomuch,thattheringsofinterestcannolongerbedistinguished,i.e.lessthan7.5Aforverticalandlessthan12Aforhorizontalpolarization.Highcurrentsmaynotbesentthroughthecoilsforalongtimesincetheymightheatup!Oncethesepictureshavebeentaken,proceedtomeasuretheradiioftheringschoosing<Circle>fromthe<Measure>menu.Forhorizontalpolarizationthethreevisibleinnerringsperordermaybeevaluated.Forverticalpolarizationtheinnertworingsofthesetofsixringsperordermaybeevaluatedsincetheyarethebestvisibleones–theotherringsarenotwellseparated.Proceedtodrawandfitcirclestoasmanyordersofringsasaresuitableinthepicture,thiswillgiveyousquaresof , ;

, ; , ;….Dothesamewiththeotherpicturescaptured.

InFig.16inthehorizontalpolarizationthesizesoftheringsofthelineswithnumber3and6accordingtoFig.7wereevaluated.Theirenergydifferenceis

so





Fig.16:Screenshotofsoftwareusedtomeasuretheradiiofinterferencerings,evaluationofhorizontalandverticalpolarisation.

InFig.17intheverticalpolarizationthesizesoftheringsofthelineswithnumber4,5,6accordingtoFig.7wereevaluated.Theirenergydifferenceis

so

with


Theaverageofbothis

Theliteraturevalueis




Fig.17:Measurementresultsfor vs.magneticfieldstrength.

Zeeman effect with an electromagnet and a CCD camera

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