TP polarization

Student'sSheet
Printed:21.08.201710:16:24|P2250100
Robert-Bosch-Breite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
Difficulty
Difficult
PreparationTime
20Minutes
ExecutionTime
10Minutes
RecommendedGroupSize
2Students
Polarisationbyquarterwaveplates(ItemNo.:P2250100)
CurricularRelevance
AdditionalRequirements: ExperimentVariations:
Keywords:
Plane,circularlyandellipticallypolarisedlight,polariser,analyser,planeofpolarisation,doublerefraction,opticaxis,ordinaryand
extraordinaryray
Introduction
Overview
Monochromaticlightfallsonamicaplateperpendiculartoitsopticaxis.Attheappropriateplatethickness( /4,orquarterwave
plate)thereisa90°phaseshiftbetweentheordinaryandtheextraordinaryraywhenthelightemergesfromthecrystal.The
polarisationoftheemergentlightisinvestigatedatdifferentanglesbetweentheopticaxisofthe /4plateandthedirectionof
polarisationoftheincidentlight.
Fig.1:Experimentalset-upfordeterminingthetypeofpolarisationoftheemergentlight.
AreaofExpertise:
ILIAS
EducationLevel:
Physik
Topic:
Hochschule
Subtopic:
LichtundOptik
Experiment:
Polarisation

Student'sSheet
Printed:21.08.201710:16:24|P2250100
Robert-Bosch-Breite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
Equipment
PositionNo. Material OrderNo. Quantity
1 Si-PhotodetectorwithAmplifier 08735-00 1
2 ControlUnitforSi-Photodetector 08735-99 1
3 Adapter,BNC-plug/socket4mm 07542-26 1
4 Lensholder 08012-00 3
5 Lens,mounted,f+100mm 08021-01 1
6 Diaphragmholder 08040-00 2
7 Irisdiaphragm 08045-00 1
8 Doublecondenser,f60mm 08137-00 1
9 Condenserholder 08015-00 1
10 HighpressureHgLamp,50W 08144-00 1
11 Powersupply230V/50Hzfor50W-Hg-lamp 13661-97 1
12 Interferencefilter,yellow,578nm 08461-01 1
13 Polarisingfilter,onstem 08610-00 2
14 Opticalbenchexpert,l=1000mm 08282-00 1
15 Baseforopticalbenchexpert,adjustable 08284-00 2
16 Slidemountforopticalbenchexpert,h=30mm 08286-01 9
17 Slidemountforopticalbenchexpert,h=80mm 08286-02 1
18 Polarizationspecimen,mica 08664-00 2
19 Digitalmultimeter2005 07129-00 1
20 Connectingcord,32A,750mm,red 07362-01 1
21 Connectingcord,32A,750mm,blue 07362-04 1
Tasks
1. Tomeasuretheintensityofplane-polarisedlightasafunctionofthepositionoftheanalyser.
2. Tomeasurethelightintensitybehindtheanalyserasafunctionoftheanglebetweentheopticaxisofthe /4plateand
thatoftheanalyser.
3. Toperformexperiment2.withtwo /4platesonebehindtheother.

Student'sSheet
Printed:21.08.201710:16:24|P2250100
Robert-Bosch-Breite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
Set-upandprocedure
TheexperimentissetupasshowninFig.1.Theexperimentlampwiththedoublecondenser(focallength60mm)fitted,the
lensholderwiththeirisdiaphragm,thelensholderwiththeinterferencefilter,thepolariser,theholderwiththe /4plate,the
lensholderwiththelensoffocallength100mm,theanalyser,andthedistributorsupportwiththesiliconphoto-cellareallset
upontheopticalbench.
Firstofallthepathoftherayisadjustedsothatthephoto-celliswellilluminated(thisisdonewithoutthe /4plate).Withthe
polariseronzero,theanalyseristhenrotateduntilthelightwhichittransmittedisofminimumintensity.The /4plateisnow
clampedintheholderandrotatedsothatthelightpassingthroughtheanalyserisagainatminimumintensity.Theplaneof
polarisationofthelightemergingfromthepolarisernowmakesanangleof0°(or90°)withtheopticaxisofthe /4plate.The
lightintensityismeasuredasafunctionofthepositionoftheanalyser,foranglesof0,30,45,60and90°,overtherange–90°
to+90°.Theresistorispluggedinparalleltotheentryofthemeasuringamplifier.
Thecurrentintensityofthephoto-cellisproportionaltotheintensityoftheincidentlight.

Student'sSheet
Printed:21.08.201710:16:24|P2250100
Robert-Bosch-Breite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
Theoryandevaluation
Fig.2:Splittingofpolarisedlightinadouble-refractingcrystal(P=polariser,A=analyser).
Thevelocityofthelighttravellinginthedirectionoftheopticaxisofadouble-refractingcrystalhasthesamevalue, ,
whateverthedirectionofitsplaneofpolarisation.Whentravellingatrightanglestotheopticaxis,polarisedlighthasthesame
velocity ,whentheelectricvectorisperpendiculartotheopticaxis(ordinaryray,seeFig.2).Iftheelectricvectorisparallelto
theopticaxisthelightvelocity (extraordinaryray).
istheamplitudeofanelectricfieldvectoremergingfromthepolariserand theanglebetweenthedirectionofpolarisation
andtheopticaxisofadouble-refractingcrystal.
FromFig.2wederivethefollowingfortheamplitudesoftheordinaryandoftheextraordinaryray:
(1)
Attime ,thestateofvibrationinthetworaysatthecrystalsurfaceisdescribedby:
(2)
Inthecaseofdouble-refractingcrystals( /4plates),thethickness
)(3)
where istherefractiveindexoftheordinaryrayand thatoftheextraordinaryrayinthecrystal,causesapathdifference
of /4(i.e.aphasedifferenceof /2)betweenthetworayswhentheycombinetoaresultantrayonemergingfromthecrystal.
From(2)weobtain
(4)
(4)istheparametricrepresentationofan vectorrotatinginthedirectionofpropagation,i.e.perpendiculartothe and
axis,aboutafixedaxis.
Foranglesof =0°and =90°weobtainplanepolarisedlightofintensity
)(5)
Foranangleof45°, ,andtheamountoftherotating vectoris

Student'sSheet
Printed:21.08.201710:16:24|P2250100
Robert-Bosch-Breite10 Tel:+49551604-0 [email protected]
D-37079Göttingen Fax:+49551604-107 www.phywe.com
)(6)
Thelightiscircularlypolarisedandofintensity
(7)
andistransmittedwithoutlossofintensityinallanalyserpositions.
Fig.3:Intensitydistributionofplane-polarisedlightasafunctionofthepositionoftheanalyser(without plate).
Atallangles otherthan0°,45°and90°,thetransmittedlightisellipticallypolarised.Thetipofthe vectorrotatingabout
theaxisparalleltothedirectionofpropagationdescribesanellipsewiththesemi-axes.
(x-direction)
(y-direction)
(8)
Fortheintensityofthelighttransmittedbytheanalyserintherespectivedirections,wehave:
(9)
Byrotatingtheanalyserweobtainthefollowingfortheratioofthemaximumtotheminimumtransmittedlightintensity:
(10)
Foranyangularsetting betweentheanalyserandtheopticaxisofthe /4plate,wehave:
(11)