LoiReflectFresnel p2250305

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Difficulty
Difficult
PreparationTime
10Minutes
ExecutionTime
20Minutes
RecommendedGroupSize
2Students
Fresnel’slaw,theoryofreflection(ItemNo.:P2250305)
CurricularRelevance
AdditionalRequirements: ExperimentVariations:
Keywords:
Electromagnetictheoryoflight,reflectioncoefficient,reflectionfactor,Brewster’slaw,lawofrefraction,polarisation,degreeofpolarisation
Introduction
Overview
Fig.1:Experimentalsetupfortheverificationoftherotationoftheplaneofpolarisationdueto
reflection(*onlyrequiredfor5mWlaser)
AreaofExpertise:
ILIAS
EducationLevel:
Physik
Topic:
Hochschule
Subtopic:
LichtundOptik
Experiment:
AusbreitungvonLicht

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Equipment
PositionNo. Material OrderNo. Quantity
1 Baseplatewithrubberfeet 08700-00 1
2 HeNelaser 08180-93 1
3 Adjustingsupport35x35mm 08711-00 2
4 Surfacemirror30x30mm 08711-01 2
5 Magnetfoot 08710-00 5
6 Polarisationfilter 08730-00 2
7 Prismtablewithsupport 08725-00 1
8 Prism,60o,flintglass 08237-00 1
9 Rotatingguiderailwithangularscaleandmagnetfoot 08717-00 1
10 Photocell,silicone 08734-00 1
11 Measurementamplifier,universal 13626-93 1
12 Voltmeter0.3...300V/10...300V~ 07035-00 1
13 Connectingcable,red,l=500mm 07361-01 2
Tasks
1. Thereflectioncoefficientoflight,whichispolarisedeitherperpendicularlyorparalleltotheplaneofincidence,istobe
determinedasafunctionoftheangleofincidenceandplottedgraphically
2. Therefractionindexoftheflintglassprismistobedetermined.
3. TherefractioncoefficientistobecalculatedbymeansofFresnel’sformulaandcomparedtothemeasuredcurve.
4. Thereflectionfactorforflintglassiscalculated.
5. Therotationoftheplaneofpolarisationforlinearlypolarisedlightafterreflectionisdeterminedasafunctionoftheangle
ofincidenceandplottedgraphically.ThisiscomparedtothevaluescalculatedbymeansofFresnel’sformula.

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Set-upandprocedure
Theexperimentalsetupisshowninfig.1.Therecommendedsetupheight(heightofbeampath)shouldbe130mm.
Setupoftherotatingunit:Tostartwith,thestoppingscrewofamagnetfootisremoved.Thecircularorificeoftherotating
guiderailissetunderthefoot.Theangularscaleissetontothemagnetfootandalsoontopoftherotatingguiderail.The
magnetfootisfixedtotheopticalbaseplate,andtherotatingguiderailcanbeshiftedsufficiently.PhotocellLDcanbe
fixedtooneendandpolarisationfilter tothemiddleoftherotatingguiderail,bothbymeansofamagnetfoot.During
thesetupoftheopticalbaseplate,theangulardistributionshouldbereasonable,thatis,the0°scalemarkshouldbe
directedtowardstheincidentlaserbeam.
PrismPrshouldbeplacedwiththeforwardsurfaceedgeexactlyonthecentralpointofthetable.Thelaserbeamisthen
adjustedontothecentralaxisoftheprismandofthetablebymeansofadjustingscrews and .
Concerningmeasurement:afterlettingthelaserwarmupforabout15minutes,experimentalsetupiscarriedoutwithout
polarisationfilter tostartwith.
Todeterminetheincidentintensity ofthelightpolarisedparalleltotheplaneofincidence(pointerofpolarizer set
to90),theprismisremovedandtherotatingguiderailisrotatedsothatthelaserbeamfallsdirectlyontothephotocell
(amplificationoftheuniversalmeasurementamplifiermustbeadjustedinsuchawaythatvoltagedoesnotincrease
abovethemaximumoutputvoltageof10V).
Aftertheprismhasbeenreplacedontotheprismtable,therotatingguiderailwithdetectorLDissettoanangle of
about10°.TheprismtablecarryingtheprismisnowturnedsothatthereflectedbeamisdirectedtowardsdetectorLD.
AccordingtoSnellius’slaw,theangleofincidenceisequaltotheexitingangle,thatis,angleofincidence ishalfthe
angle formedbytheincidentlaserbeamandtherotatingguiderail.
Theangleoftherotatingguiderailisnowmodifiedinstepsof5°(stepsofabout2.5°intheareaofBrewster’sangle).The
prismisturnedeverytimeinsuchawaythatthelaserbeamfallsonthedetector,inordertodeterminelightintensity .
Angle shouldbevarieduptoabout160°.
Thisexperimentisrepeatedwithlightpolarisedperpendicularlytotheplaneofincidenceoftheprism(pointerofpolarizer
setto0°).Forthis,theintensityoftheincidentlaserbeamwithoutprism, mustbedeterminedtostartwith.
Concerningthe2ndpartofmeasurements:polarisingfilter isbroughtintothebeampathbetweenprismandphotocell
ontherotatingguiderail.Polarizer issettoanangleof45°(pointersetto45).Withoutprism,detectorLDwould
indicateanintensityminimumifthepolarisingdirectionsofthetwopolarisingfilters and werecrossed( pointer
at-45°).Onemakesuseofthefactthattheintensityminimumcanbedeterminedmorepreciselythanthepeak,sothat
duringreflectionattheprism,onlooksfortheintensityminimumthroughrotationofpolarisingfilter .Therotation
supplementaryto-45°istherotationoftheplaneofpolarisation duetoreflectionattheprism.Thisiscarriedoutfor
differentanglesofincidence ofthelaserbeamonthesurfaceoftheprism.Variationoftheangleofincidenceiscarried
outasinthefirstpart.

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Theoryandevaluation
Inalightwave,theelectricfieldvector andthemagneticvector oscillateperpendicularlyandinphasetoeachother.
IntensityisgivenbyMaxwell’sequation:
(1)
where istherefractionindexofthemediumthroughwhichthelightbeamtravels.Theenergyofthewavetransportedinthe
directionofpropagationisgivenbyPoynting’svector,accordingtothefollowingrelation:
und (2)
Iflightfallsontoaboundarysurfaceofanisotropicmediumofrefractionindex withanangleofincidence ,partofthe
intensityisreflectedandtherestgoesthroughthemediumunderanangleofrefraction .Thefollowingindexesareusedinthe
theorymentionedbelow:
directionofoscillationoftheelectricandmagneticfiledvectors,whicharedirectedeitherparallelorperpendicularlytothe
angleofincidence.
Incident,reflectedandrefractedvectorcomponents.Infig.2A),theelectricfieldvector
oftheincidentlightwaveoscillatesperpendicularlytotheplaneofincidence;accordingto(2),magneticvector oscillates
paralleltothelatter.Relatedtothelawofcontinuityofthetangentialcomponents(thatis,thecomponentswhichoscillate
paralleltothesurfaceoftheobject)andtothedirectionofthebeam,thefollowingrelationholds:
Fig.2:A)directionofoscillationoftheelectricfieldvectorperpendicularlyandB)paralleltothedirectionofincidence
(3)
With(1)and(3)oneobtains:
(4)
Takingintoaccountthelawofrefraction,therelationoffieldintensitiesis:
(5)
where isdefinedasreflectioncoefficient.
Fig.2B)showsanincidentlightwave,whosevector oscillatesperpendicularlytotheplaneofincidence.
Thefollowingisobtained,similarto(3):

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(6)
(7)
(8)
Fresnel’sformulae(5)and(8)canbewritteninadifferentform,eliminatingrefractionangle bymeansofSnellius’lawof
refraction:
(9a)
(9b)
isvalidforallanglesofincidence betweenzeroand .
Specialcases
A:thefollowingrelationisvalidforperpendicularincidence( ):
(10)
B:foragrazingangle ,thefollowingholds:
(11)
C:ifthereflectedandtherefractedbeamsareperpendiculartoeachother ,asshowninfig.3,therefollowsfrom
(8):
Fig.3:Brewster’slaw
(12)
thatis,reflectedlightiscompletelypolarised.Inthiscase,theelectricvectoroscillatesonlyperpendicularlytotheplaneof
incidence.RelatedtoSnellius’lawofrefraction,thefollowingisvalid: