faraday rotation

7/17/2019 Faraday Rotation

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Faraday Rotation


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Literally bending (twisting) light.

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Step 1: Introduction: Circular MagneticBirefringence
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This project recreates Faraday's 184 e!periment that re"ealed the

#$ndamental nat$re o# light% electromagnetic wa"es&

istory%

In 1845, Mihael !araday "sed a #ower$"l eletromagnet to rotate the#olari%ation o$ a beam o$ light, "ni$ying eletromagneti $ore with light in one o$the most elegant and seminal eeriments ever.

'wo deades later, ames Ma&well on$irmed this with his lassialeletromagneti e"ations whih showed that light is at"ally an eletromagneti

wave. It wasn*t "ntil the 1+-s, however, that !araday rotation was modeled"ant"mmehanially.

'oday, this e$$et is alled the !araday e$$et or !araday rotation. /ee the lastste# in this instr"table $or realli$e a##liations.

A(o$t this project%

0 !araday rotator is a devie that rotates the #lane o$ #olari%ation o$ linearly#olari%ed eletromagneti waves (s"h as visible light) #assing thro"gh matter (adieletri an ins"lator) by a##lying a magneti $ield #arallel to the diretion o$#ro#agation o$ the light. ('his is a very in$ormativelin23htt#3www.teahs#in.ominstr"ments$aradayinde&.shtml )

I am "rrently eerimenting with the $"lly $"ntional devie that I have b"ilt. Imade this devie to demonstrate !araday rotation and I am still wor2ing on
http://www.teachspin.com/instruments/faraday/index.shtmlhttp://www.teachspin.com/instruments/faraday/index.shtml


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learning the #hysis behind it in greater de#th. 'his is my senior #roet $or my6I/7 7nglish lass. ie, eh9 I get to do :hysis $or an 7nglish lass;

It will ost a bare minim"m o$


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0asers%

I highly suggest you read this before using any laserever:http://www.repairfaq.org/sam/lasersaf.htm

ever loo2 into the beam o$ any laser (this one sho"ld be a nobrainer)

ever #oint any laser at any #erson, vehile, animal, et. (also a nobrainer)

Nse e&treme #rea"tion when "sing high #owered lasers (anything above5m6)

Nse e&treme #rea"tion when "sing IR (in$rared) or NF ("ltraviolet) lasers(these wavelengths are not visible to the h"man eye, so the "s"al blin2 re$le&
http://www.repairfaq.org/sam/lasersaf.htmhttp://www.repairfaq.org/sam/lasersaf.htm


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annot #rotet yo" i$ a 5m6 beam bo"nes into yo"r eye) 0lways "se #ro#er eye #rotetion rated $or the orret wavelength and #owero"t#"t o$ yo"r laser(s)

0lways "se a $i&ed, nonre$letive obet to sto# the beam o$ any laser over5m6

Nse a s#eial room with restrited aess, no re$letive s"r$aes, and allo#enings $"lly overed by thi2 bla2 $abri $or high #ower

eodymi$m *agnets%

Read this3 htt#3www.2magnetis.omsa$ety.as#

:inhsmashs"ishshattersevere in"ry ha%ardO be very are$"l. I have a$riend who wor2s at a om#any that #"ts together #ower$"l magneti assemblieswho nearly lost a hand to a #air o$ = "bes.

I$ yo" want to se#arate magnets or reattah magnets, slide them a#art. Do"an #"t the sta2 o$ magnets on the edge o$ a table and #"sh down to do slidethem a#art. ever try to reattah magnets to eah other by moving the $aestogetherO this is more dangero"s.

Pee# them away $rom 'Fs, om#"ters, redit ards, and eletronis or they willr"in yo"r st"$$.

igh oltage #or ee 0asers and other things%

Read this3 htt#3www.re#air$a.orgsamsa$ety.htm

Nse a"tion and ommon sense.

'"rn ono$$ with the swith on a #owerstri#.

!or


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(MQ's). 'hey #"t o"t only >2F at SEVERA A!"S. #$%IS &I 'I ()*+,

Pee# one hand in a #ants #o2et at all times when "sing any high voltageO thiswill hel# limit the amo"nt o$ "rrent that an go thro"gh yo"r heart i$ yo" areaidentally sho2ed.

6ear #ro#er eye #rotetion

ever #lay with the #ower mains. #-AR&I A&AR- !A$ERIA)

*achine Shop and and Tools%

0lways wear #ro#er eye #rotetion.

It sho"ld go witho"t saying, b"t "se ommon sense. 6hen "sing #ower tools (s"h as drill#ress, lathe, mill, grinder, bandsaw,tablesaw, et), do Q' wear gloves. 'he mahine an #"ll in a loose glove 0Byo"r handarm. I$ yo" ath "st yo"r $lesh in a mahine, it will tear leanlyinstead o$ s"2ing yo" into the mahine. 6hile yo" o#erate mahines, wearlose$itting lothing, tie ba2 long hair, and remove yo"r ewelry.

Nse #ro#er gloves when yo" handle shar# metal items and when "sing hand

tools s"h as a ra%or2ni$e. 0lways "se set sa$ety g"ards on mahines to the #ro#er height.

ever wor2 alone. ever wor2 when yo" are tired or very stressed. 6or2 in a very well ventilated room or o"tside i$ yo" are "sing to&i or volatile#aints, solvents, gl"es, et. Nse a #a#er$ilterty#e mas2 $or sawd"st and other #arti"lates that $loat

aro"nd in the air.

Step 3: Materials


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1 glass rod3

'his r"ial element o$ the devie m"st be 'erbi"m do#ed borosiliate glass or'erbi"m ?alli"m ?arnet ('??) or some similar #aramagneti material with avery high Ferdet onstant in order to #rod"e a meas"rable e$$et. 'hehea#est so"re $or this is htt#3www.teahs#in.ominstr"mentsN/H0S=-#ries.shtml$araday(


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om#any that tosses a lot o$ magnets d"e to small hi#s or hanges in "stomers#ei$iations. I have also #"rhased inredibly strong magnets$romhtt#3www.2magnetis.om

R%

1 power#$l solenoid3 15cm long3 with a high c$rrent power s$pply%

0s yo" an see in my #hotos, I handwo"nd a large solenoid on a ardboard t"bethat I made $rom a manila $older. 'he magnet wire ame o"t o$ the trans$ormerthat I "t a#art to get the steel $or the horseshoe magnet. 'he solenoid an r"non 14.5F BH T >0 $or abo"t = min"tes be$ore I an start to smell something

melting. It ertainly wo"ld be a more elegant way to ma2e a !araday rotator bea"se yo" wo"ld be lin2ing eletriity and magnetism in addition to lin2ingmagnetism and light.

R%

1 long3 a!ially magneti6ed ring magnet%

I have not tried this, b"t I thin2 that it wo"ld be a great way to ma2e a reallystrong $ield. Cowever, yo" have no way to ad"st the $ield strength. Do" an#"rhase a sta2 o$ 1 o$ these $or .=5. Aased on the hel#$"l $ieldvis"ali%ations on the #rod"t #age (htt#3www.2magnetis.om#roddetail.as#9#rodERH445=), this wo"ld have an average magneti $ield #arallel to the#ro#agation o$ the light o$ an inredible .5 'esla or so.

2 linear polari6ers%

:olaroid sheet wor2s great. I "sed 4 #olari%ers bea"se they aren*t e&tremelye$$iient at #olari%ing bl"e light. 'hey are #retty hea#.(htt#3www.ama%on.om/"areLinear:olari%ed!ilter6indowd#A--48->!0P)

1 protractor%
http://www.kjmagnetics.com/http://www.kjmagnetics.com/proddetail.asp?prod=RC44-N52http://www.kjmagnetics.com/proddetail.asp?prod=RC44-N52http://www.amazon.com/Square-Linear-Polarized-Filter-Window/dp/B004803FAKhttp://www.amazon.com/Square-Linear-Polarized-Filter-Window/dp/B004803FAKhttp://www.kjmagnetics.com/http://www.kjmagnetics.com/proddetail.asp?prod=RC44-N52http://www.kjmagnetics.com/proddetail.asp?prod=RC44-N52http://www.amazon.com/Square-Linear-Polarized-Filter-Window/dp/B004803FAKhttp://www.amazon.com/Square-Linear-Polarized-Filter-Window/dp/B004803FAK


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It needs to be able to meas"res to hal$ a degree.

0asers% The Faraday e##ect has di##erent degrees o# magnit$de #or di##erent

wa"elengths o# light&

I bo"ght htt#3gi.ebay.om4J>nmAl"eLaserB://A6'e2A6A1-Q7M==--->5-J#tELC@Be$a"ltBomain@-hashEitem>>-5d5d1> to allowme to eeriment with another wavelength o$ light. It is a bea"ti$"l B:// (diode#"m#edsolidstate) 4J> nm (t"r"iose) 5 m6 (sa$e, low #ower) lablaser. 0nother reason I bo"ght this laser was to ma2e this #roet as ool as#ossible as I will be donating the devie to the siene de#artment at my highshool as a tool to get st"dents interested in #hysis.

0 4-5nm bl"eviolet laser #ointer is a m"h hea#er so"re o$ a shorterwavelength o$ visible light. Cowever, I $o"nd that it doesn*t wor2 $or thiseeriment bea"se 4-5 nm light ma2es the glass rod $l"orese so intenselyyellow that none o$ the beam at"ally gets thro"gh the rod.

I also bo"ght a = m6 Cee (Celi"meon) laser t"be $or abo"t


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Qne =* & 4* #iee o$ #egboard (the sheet with all the 1 evenly s#aed 14 holesin it) this is the standard si%e.

Lots o$ 1 thi2 #ine wood ($or mo"nting #olari%ers, glass rod, #hotosensor,magnet) 0lso, i$ yo" get a A6 'e2 A6A1-Q7M 4J> nm5 m6 laser, then yo" an "se this wood (or >4thi2 wood) to ma2e a bo& $orthe #ower s"##ly yo" may also want #le&iglass or#re$erably #olyarbonate $or the to#, woodsrews to hold it together, and hotgl"eto #"t on the brittle #le&iglass. I$ yo" "se woodsrews to #"t together a bo&, de$inately drill #ilot holes the si%e o$ the srewshan2 to avoid s#litting the wood.

0bo"t =5 reg"lar steel 14=- n"ts.

0bo"t - reg"lar steel 14 IB washers.

0bo"t =5 reg"lar 14=- bolts, 1.5 long.

=4 reg"lar 14=- bolts, > long.

= 14=- wingn"ts.

= 14=- wingbolts or bolts that yo" an tighten by hand, 1.5 long.

/mall diameter al"min"m #i#e $or s#aers $or the 4J>nm lab laser.

0bo"t 8 small s"are = & 4s and abo"t 1 nails (s"##orts $or the main board).

Step 4: Tools


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ower Tools%

Cand drill $or ma2ing holes in the wooden mo"nts and the #egboard. Qnly a14learane bit is needed.

Aandsaw $or "tting wood, #olyarbonate, #egboard, et.

and Tools%

Cammer $or nailing the wood s"##ort blo2s onto the #egboard and the steel#art o$ the horseshoe magnet onto the wood mo"nt.

Ca2saw $or "tting wood, #egboard, #olyarbonate, nails that are too long, et.

'wo J1 wrenhes.
http://www.instructables.com/id/Faraday-Rotation-EPIC/?ALLSTEPS#more-anchorhttp://www.instructables.com/id/Faraday-Rotation-EPIC/?ALLSTEPS#more-anchorhttp://www.instructables.com/id/Faraday-Rotation-EPIC/?ALLSTEPS#more-anchor


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:i#e "tter $or ma2ing al"min"m t"be s#aers to mo"nt the bl"e lab laser.

6ire stri##ers $or stri##ing the ins"lated leads on the sensor.

*eas$ring Tools%

onmagneti metri ta#e or r"ler $or meas"ring the distane between thehorseshoe magnet and the laser beam in the glass rod.

/tandard7nglish ta#e meas"re.

/har#ie $or mar2ing things.

M"ltimeter $or meas"ring the voltage #"t o"t by the reg"latorsensor diode. Igot mine $rom ir"it s#eialists $or


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1: ;ecide on a height #or the laser (eam


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se"rely in #lae.

0 mo"nt $or the sensordiode. "st bolt the sensor on i$ yo" have the 2ind Ihave. 0lternatively, yo" o"ld "st "se an L7B it will at as a tiny solar ell.

0 mo"nt $or the magnet steel H. My steel #iee $rom the trans$ormer amewith holes in the orners, so I "st nailed it on. It is im#ortant that this mo"nt anslide on slots in the #egboard so that yo" an vary the magneti $ield and viewthe !araday e$$et.

0 mo"nt $or the laser. 'his may be wood, b"t $or my 4J> nm 5 m6 lab laser I"sed al"min"m t"bing to ma2e s#aers and I "st bolted it right on.

0 #oorman*s o#tial table o"t o$ #egboard and wooden blo2 s"##orts that are

nailed on the bottom. Ma2e s"re it is "st the si%e yo" want itO too big is betterthan too small. Ca2saw the #egboard and nail on wooden blo2s to the ornerswith = nails eah. I added an e&tra blo2 later near the glass rod mo"nt to sto#the board $rom $le&ing, b"t wait "ntil yo" are done with assembly so that yo" willnot #"t a nail or a wooden blo2 s"##ort where it will get in the way o$ a bolt.

0 wooden bo& $or the laser #ower s"##ly. 'his entails onneting the twointerlo2 wires as well as eletrialta#ing eosed metal and bare wires thatarry 1=-F 0H. :olyarbonate is best $or ma2ing a lear to# $or the bo&. Nsewood srews to attah the sides o$ the bo&O remember to drill #ilot holes the si%e

o$ the srew shan2 to #revent the wood $rom s#litting.

2: Attaching components to their mo$nts%

?Ca2saw a slot in the mo"nt $or the $irst linear #olari%erO hot gl"e it in.

Ca2saw a slot in the mo"nt $or the seond linear #olari%erO hot gl"e in the#rotrator and #"shta2 on the seond linear #olari%erO ma2e s"re thateverything is lined "# well. Hlam#hold "ntil gl"e drieshardens.

6ait to %i#tie on or otherwise attah the glass rodO it is eensive and easilydamaged, so wait "ntil the entire devie is assembled.

Aolt on the sensor to the wooden mo"nt. I$ yo" are "sing an L7B, yo" an drilla hole thro"gh the mo"nt and hot gl"e the L7B in the ba2 o$ the hole ($rom theba2 o$ the mo"nt).


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:"t the laser bolts thro"gh the laser and thro"gh the s#aers. It is neessary to"se a tinsni#s to modi$y a washer to $it that lose to the laser mod"le body.

H"t al"min"m t"bing s#aers $or bolts that will $ritionhold the laser #owers"##ly bo& onto the #egboard.

Step ": #sse$%ly


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1: Attach the laser mod$le and the power s$pply (o!&

0ttah bolts with s#aers and washers aro"nd the bo& on the #egboard, ma2ings"re that it ma2es a tight $rition$it.

Aolt the laser mod"le onto the #egboard with long bolts, s#aers, and washers.

2: Attach the #irst linear polari6er&

Aolt it onto the #egboard in $ront o$ the laser mod"le.

@: Attach the glass rod mo$nt&

Aolt it onto the #egboard in $ront o$ the the $irst linear #olari%erO 2now that the


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glass rod m"st line "# with the laser beam.

4: Attach the second linear polari6er and protractor mo$nt&

Aolt it onto the #egboard on one end o$ the glass rod mo"nt.

: Attach the optical sensor and (eam


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.eneral Tips=S$ggestions%

ever tighten one bolt on a mo"nt all the the way be$ore tightening the other atall. Instead, tighten them eah bit by bit, sim"ltaneo"sly.

Pee# things loosened "ntil yo" are s"re that they need to be e&atly where theyare.

Bon*t attah the eensive glass rod "ntil the very endO this will really hel##rotet it $rom being bro2en.

Ae very are$"l when ad"sting the magnets on the sliding slotsO i$ yo" leave themagnet loose it may smash into the glass rod.

Nse woodenblo2 s"##orts nailed to the bottom o$ the #egboard to hel# theo#tial system maintain its rigidity.

Do" may have to slot some things to ma2e them line "# "st right.

'he holes in the #egboard are e&atly 14, not 14learane. Do" may wantto drill them o"t so that bolts $it thro"gh easily. I did not do this bea"se there areso many holes.

Nse washers on to# o$ wooden mo"nts and on the bottom o$ the #egboard.

oin a !IR/' Robotis Hom#etition (!RH) teamO this will give yo" all the s2illsyo" will need to ma2e something with yo"r hands and the neessary tools.

Step &: #ligning and Testing t'e (ptical Syste$

ptical (enches cost too m$ch3 and optical ta(les cost way too m$ch&

There#ore3 the (est option is to rig $p yo$r own poor


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peg(oard on wooden s$pports& owe"er3 this can (e pro(lematic3 as

peg(oard is not especially rigid&

I# yo$ ha"e a smo)e machine or can (orrow one3 that co$ld really ma)e

things a (it easier3 as it will allow yo$ to see the (eam o# a low powered

"isi(le) Line "# the glass rod so that the beam both enters and e&its the rod e&atly atthe enter o$ the ir"lar end. It may be neessary to slot the mo"nt. Aee&tremely are$"l with the glass rod. 'ighten down the bolts on the glass rodmo"nt.

4) Ma2e s"re that both linear #olari%ers are #ositioned so that the beam goesthro"gh them. Hhe2 that the seond linear #olari%er an move $rom abo"t 1-degrees to K>- degrees with the laser beam still going thro"gh the at"al

#olaroid #art o$ the s"are slide and not getting blo2ed by the#a#erardboard #art o$ the s"are slide.

5) '"rn the laser o$$. Do"*re done.

Step ): Testing and Trou%les'ooting


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I# yo$ ha"e any B$estions or pro(lems3 #eel #ree to send me a message on

instr$cta(les and I will do my (est to assist yo$&

Step *: Finis'ed+ ,-o. t'e data andcalculations/0


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,!planation o# the eB$ation in the second photo a(o"e%

Aeta is the angle o$ rotation.

F is the Ferdet onstant, whih tells yo" abo"t the magnetoo#tial #ro#ertieso$ a s#ei$i material at a s#ei$i wavelength

A is the strength o$ the magneti $ield #arallel to the #ro#agation o$ the light

d is the distane that the light #ro#agates thro"gh the material.

ow that I ha"e #inished ($ilding the de"ice3 I am starting to e!perimenting

with itD testing "ario$s "aria(les s$ch as%

wavelength o$ light "se di$$erent lasers

strength o$ the magneti $ield #arallel to the #ro#agation o$ the light move the


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horseshoe magnet

tem#erat"re o$ the rotator material I*m not s"re how I will do this yet. 7&tremetem#erat"res might ra2 the glass rod.

*eas$ring the magnet%

In order to vary the magneti $ield strength, I am testing the magnets with a Calle$$et #robe borrowed at Hornell, nearby. I $o"nd that the s"r$ae $ield o$ myhorseshoe magnet is a who##ing .5J 'esla. ote that this is the magneti $ieldstrength #er#endi"lar to both the #oles"r$aes and the #ro#agation o$ the light.

0 Calle$$et #robe (?a"ss #robe) has the #ro#erty that rotating it will meas"rethe om#onent o$ the magneti $ield in that one diretion. (/ee gra#h above)

ote that in order to $ind the average #arallel magneti $ield at di$$erentdistanes, it is neessary to "se the 'ra#e%oidr"le or /im#son*s r"le to integratethe varying magneti $ield over the length o$ the glass rod, and then divide yo"rtotal by the entirelength. htt#3mathworld.wol$ram.om/im#sonsR"le.html htt#3mathworld.wol$ram.om'ra#e%oidalR"le.html (/ee gra#h above)

I "sed a 'ra#r"le, meas"ring on the a&is onneting the #oles and $inding theaverage magneti $ieldO I then moved the Calle$$et #robe along the the same

a&is onneting the #oles, sto##ing when the #robe registered a magneti $ielde"al to the average magneti $ield (at the same distane $rom the a&isonneting the #oles). 'hen, I meas"red every hal$entimeter o"t $rom that a&is(#er#endi"lar to the a&is onneting the #oles.) 'hen I gra#hed thea##ro&imate average magneti $ield strength as a $"ntion o$ distane $rom themagnet.(/ee gra#h above)

Meas"ring the !araday rotation3

Meas"re the angles o$ !araday rotation with the magnet at di$$erent distanes$rom the beam, "sing the same wavelength o$ light. :lot yo"r angles against themagnet distane. (/ee gra#h above)

Do" an then #lot the angles o$ !araday rotation against the a##ro&imateaverage magneti $ield that yo" already #lotted as a $"ntion o$ distane. 'heslo#e sho"ld be the Ferdet onstant o$ the glass rod material at the #arti"lar
http://mathworld.wolfram.com/SimpsonsRule.htmlhttp://mathworld.wolfram.com/TrapezoidalRule.htmlhttp://mathworld.wolfram.com/TrapezoidalRule.htmlhttp://mathworld.wolfram.com/SimpsonsRule.htmlhttp://mathworld.wolfram.com/TrapezoidalRule.htmlhttp://mathworld.wolfram.com/TrapezoidalRule.html


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wavelength, times the length o$ the glass rod in meters. 0$ter editing o"t > #ointsnear the edge o$ the magneti $ield a##ro&imation, I got 1+ radians #er 'eslameter as my al"lated val"e $or the Ferdet onstant o$ the glass rod $or 5- nmlight. 'he 2nown val"e is => radians #er 'eslameter $or 5- nm light in thisglass rod. My error was only 1J.4S. (/ee gra#h above)

I$ yo" have more than one laser, yo" an #lot the angle o$ !araday rotationagainst the wavelength o$ the light allowing yo" to #lot the Ferdet onstant o$the #arti"lar material as a $"ntion o$ wavelength. 'he Ferdet onstant is alsoavailable $rom the s"##lier o$ the glass rod. I also "st $o"nd a gra#h o$ theFerdet onstant $or this material (/!5+ glass) as a $"ntion o$ wavelengths.(/ee gra#h above)

And #inally%

Learn abo"t how !araday rotation wor2s (see the ne&t ste#). /how yo"r !aradayrotator to yo"r $riends. Bonate it to yo"r high shool.

Step 1: Real orld #pplications

According to the Teachspin

we(sitehttp%==www&teachspin&com=instr$ments=#araday=inde!&shtml3 Farada

y rotation has a practical application in optical isolators&

0n o#tial isolator is a devie that allows light to go thro"gh in one diretion b"tseverely atten"ates re$leted light #ro#agating in the o##osite diretion. Modern

"ltrahigh $ield #ermanent magnets and s#eial #aramagneti glasses havemade these devies "ite small, b"t not hea# (abo"t


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o#eration o$ the laser itsel$.

Also3 Faraday rotation is $sed to detect magnetic #ields in interstellar

space&

'o do this, astronomers#hysiists have to estimate the eletron density o$ thes#ae that they are e&amining, and s"m "# the "m"lative e$$ets o$ all magneti$ields (#arallel to the #ro#agation o$ the light) between the so"re and where themeas"rements o$ #olari%ation are arried o"t, on 7arth.

In interstellar s#ae, the angle o$ rotation is #ro#ortional to the n"mber o$eletrons that the light hits times the strength o$ the magneti $ield (#arallel to the#ro#agation o$ the light) m"lti#lied by (integrated over) the distane that the light

travels in the $ield, divided by the wavelength o$ light s"ared. Ay om#aring andanaly%ing the relative degrees o$ #olari%ation at vario"s di$$erent wavelengths,astronomers an ma# o"t magneti $ields $ar o"t in the "niverse; (0t least whatthey were when the light #assed thro"gh them, whih o"ld have been a verylong time ago.)

Step 11: o. T'ings or: # Classical6planation


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This paper has the (est simpli#ied classical e!planation that I co$ld #ind%

http%==we(&mit&ed$=8&1@==/0,!periments=/0,!pE58&

,!planation o# what the paper means%
http://web.mit.edu/8.13/WWW/JLExperiments/JLExp_08.pdfhttp://web.mit.edu/8.13/WWW/JLExperiments/JLExp_08.pdf


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'he #a#er models eah eletron in the 'erbi"mglass material as a hargedmass on a s#ring, with a veloity #er#endi"lar to the #ro#agation o$ the light(and the magneti $ield). 'he s#ring re#resents the attrative eletri $orebetween the n"le"s o$ the atom and the eletron. 'his ideal s#ring has ane"ilibri"m #osition o$ length e"al to %ero. (/ee diagram above)

Light #ro#agates, or moves thro"gh s#ae, along the &a&is, by onvention. 'he% and y a&es are #er#endi"lar to eah other and to the & a&is. Light is aombination o$ an eletri $ield whose magnit"de varies sin"soidally with the#ro#agation o$ the light, and a #er#endi"lar (transverse) magneti $ield whoseintensity also varies sin"soidally with the #ro#agation o$ the light. 'he ma&im"mmagnit"de o$ 7 (the eletri $ield) is e"al to the ma&im"m magnit"de o$ A (themagneti $ield) divided by (the s#eed o$ light in a va""m, =++,J+=,458 ms).Fisible light is one ty#e o$ eletromagneti wave. (/ee diagram above)

Linearly #olari%ed light is an eletromagneti wave whose eletri $ield ison$ined to one #lane and whose magneti $ield is on$ined to another #lane thatis #er#endi"lar to the $irst. Linear #olari%ed light is th"s alled a #lane wave.(/ee diagram above)

Hir"larly #olari%ed light is om#osed o$ two #lane waves o$ e"al am#lit"de b"tdi$$ering in #hase by +- or =J- degrees. 'he s"m o$ the two #eriodi eletri$ield vetors gives a net eletri $ield vetor with onstant magnit"de, and that isrotating either lo2wise or o"nter lo2wise (both $rom the #oint o$ view o$ the

light so"re), de#ending on whether the #hase di$$erene is +- degrees or =J-degrees. Righthanded ir"larly #olari%ed light and le$thanded ir"larly#olari%ed light have eletri $ield vetors that s#iral in o##osite diretions as thelight #ro#agates thro"gh s#ae. (/ee diagram above)

6hen wor2ing with the at"al devie, the linear #olari%ation is onsidered to bethe diretion o$ the Ga&is (the one with the eletri $ield). 0n e"al ombinationo$ right and le$t handed ir"larly #olari%ed light waves, in #hase with eah other,add "# e&atly to a linear #olari%ed light wave. 'his is bea"se the hori%ontal#lane waves are 18- degrees o"t o$ #hase with eah other and will th"s anel

eah other o"t. 'he vertial #lane waves, whih are in #hase with eah other,"st give a net vertial #lane wave that has twie the am#lit"de.

'he eletri $ield a##lies an attrative or re#"lsive $ore on the eletron. Aea"sethe rotating $ield vetor o$ the ir"larly #olari%ed light is #eriodi in nat"re in the%y #lane (#er#endi"lar to the #ro#agation), it will a##ly a #eriodi $ore on theeletron, a"sing it to eeriene a #eriodi dis#laement in said #lane. 'his


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#eriodi dis#laement o"rs in o##osite diretions $or right hand and le$t hand#olari%ations, bea"se the #eriodi eletri $ield is yling in o##osite diretions.'his res"lts in the eletron being dis#laed some distane $rom its e"ilibri"m#osition at all times.

Cowever, linearly #olari%ed light wo"ld only a"se a #eriodi "#down motion o$the eletron on the Us#ring.V I$ one averages the net dis#laement o$ the eletronover time, it wo"ld be %ero. 'h"s, the eletron "st #eriodially gains and losesenergy, with a net hange in its energy o$ %ero.

'he am#lit"de o$ the eletronWs ang"lar motion (or e"ivalently, in the ase o$linearly #olari%ed light, the dis#laement $rom the eletronWs e"ilibri"m #osition)is diretly #ro#ortional to its energyO the energy is stored in the Us#ring.V 'h"s,when the eletri $ield o$ the ir"larly #olari%ed light wave ats on the eletron, it

m"st either add or s"btrat (de#ending on its handedness) $rom the eletron*senergy.

'his energy that the eletron gains is lost $rom the light, a"sing the am#lit"de o$the light to derease (or the wave dissolves altogether). ormally, with noe&ternal magneti $ield #resent, the linearly #olari%ed light wave is reemitted bythe #eriodially moving eletron. 'he #eriodially moving eletron nat"rallyreates a sel$#ro#agating eletromagneti wave3 it reates a #eriodi eletri$ield d"e to its harge and #eriodi motion, and a transverse #eriodi magneti$ield d"e to its harge, veloity, and #eriodi motion. 'his a"ses the s#ring to

ret"rn to its original #osition, the eletron to again reah its e"ilibri"m #osition,and the eletron to lose its #revio"sly gained energy. 'his light wave is identialto the original right or le$t handed #olari%ed light wave that $irst interated with theeletron.

I$ there is a magneti $ield, the reemitted wave will be di$$erent $rom theabsorbed wave. Aea"se the a$$eted eletron has been given a veloity#er#endi"lar to the a##lied magneti $ield by the #eriodi eletri $ield o$ their"larly #olari%ed light wave, it eerienes a $ore "# that strethes thes#ring a little bit $arther "# or down. (Remember that the eletron is already

eeriening a ir"lar #eriodi motion and has an "n"s"ally high or low energyd"e to the #eriodi eletri $ield $rom the ir"larly #olari%ed lightO the s#ring hasalready been strethed by the light.) 'he $ore on a moving harged #artile ise"al to vA, whih is the harge o$ the #artile times the veloity o$ the #artiletimes the magnit"de o$ the magneti $ield that is #er#endi"lar to the veloity o$the harged #artile. 'his $ore is what a"ses the small inrease or derease inthe eletron*s energy, de#ending on the diretion o$ the $ore whih de#ends


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on the diretion o$ the eletron*s veloity whih de#ends on the handedness o$the ir"larly #olari%ed light that interated with the eletron.

6hen the s#ring #"lls the eletron ba2 to its original e"ilibri"m #osition, theeletron loses energy and emits an eletromagneti wave, "st li2e in the asedis"ssed earlier where no e&ternal magneti $ield is #resent. Cowever,de#ending on the handedness o$ the light, the eletron $alls a slightly di$$erentdistane (the s#ring releases a slightly di$$erent amo"nt o$ energy). 'here$ore,the ir"larly #olari%ed light waves that are released have slightly di$$erentwavelengths, as the energy o$ an eletromagneti wave is inversely #ro#ortionalto its wavelength.

'he inde& o$ re$ration is n, whih e"als , the s#eed o$ light in a va""m,divided by the s#eed o$ the light #ro#agating thro"gh the medi"m. 0s do many

materials, the glass rod medi"m inherently has di$$erent inde&es o$ re$ration atdi$$erent wavelengths o$ light. 'his an be elained by the di$$erent losses o$energy $rom the osillating eletri $ield to the eletron, whih is made toosillate. 'he loser the $re"eny o$ the light (a onstant times one over thewavelength) to the nat"ral resonant $re"eny o$ the eletron as a mass on as#ring (de#ends only on mass and s#ring onstant), the more energy lost to theosillating eletron and the higher the am#lit"de o$ the eletron. 'he higher theam#lit"de o$ the eletron*s #eriodi motion, the longer it ta2es the eletron to reemit the absorbed eletromagneti wave, and th"s the longer it ta2es $or the lightto #ro#agate thro"gh the medi"m a ertain distane. 'he slower #ro#agation is

e"ivalent to a higher inde& o$ re$ration. 'he #henomenon o$ di$$erent inde&eso$ re$ration e&isting $or light at di$$erent wavelengths in a medi"m is alleddis#ersion.

/o, when one gets the two a$orementioned ir"larly #olari%ed waves withslightly di$$erent wavelengths #ro#agating in s"h a medi"m, d"e to the a##liede&ternal magneti $ield o$ the #ermanent magnets, one travels slightly $aster thanthe other d"e to dis#ersion. !inally, this in t"rn a"ses these two waves tobeome slightly o"t o$ #hase.

'he s"m o$ two ir"larly #olari%ed waves o$ e"al magnit"de that are o"t o$#hase is a rotated linearly #olari%ed wave and a le$tover le$t or right handedir"larly #olari%ed om#onent. 6hen this mi& o$ waves reahes the :olaroids,only the rotated linearly #olari%ed light an #ass thro"gh, and the le$toverir"larly #olari%ed om#onent is sreened o"t. 'h"s, one an observe thea##arent rotation.


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S$mmary%

Nltimately, it is the s#iraling eletri $ield vetors o$ the two #olari%ed lightom#onents o$ the linearly #olari%ed light that give the eletrons their veloities inthe %y #lane and th"s allow the a##lied e&ternal magneti $ield to at on theeletrons, a"sing them to lose slightly di$$erent amo"nts o$ energy and to th"sreemit light at slightly di$$erent wavelengths. 'hen, d"e to the nat"ral dis#ersiono$ the medi"m, the two ir"larly #olari%ed waves beome o"t o$ #haseO theythen will add to net a slightly rotated observable linearly #olari%ed waveom#onent and a small le$tover right or le$t handed ir"larly #olari%edom#onent that annot #ass thro"gh the seond linear #olari%er.

faraday rotation

Documents

rotation epic

beam o

diretion o

agation o

lane o

araday e

bare minimm o

visible light