Optics Tutorial LAK

8/13/2019 Optics Tutorial LAK

1/32

Basic OpticsLaura KranendonkERC, UW Madison

2004

Table of Contents

Basic Optics

1. Introduction 1

2. Proerties o! Li"#t.. 1

a. Co$or 1%. &ectra$ Po'er 2

c. Po$ari(ation. 4

). *tica$ +undaenta$s. 4a. +erat-s Princi$e

%. &ne$$-s La'. /c. +resne$ Euations.

d. Etendue e. Co#erence 11

!. &catterin". 1)

Optical Laboratory Toolbox

1. Introduction. 1

2. Creatin" Li"#t.. 1a. Lasers.. 1

%. LE3s.. 1

). 3irectin" Li"#t.. 1a. LensesMirrors. 1

%. +i%ers.. 22

4. Contro$$in" Wa5e$en"t#. 24

a. 3i!!raction 6ratin". 24%. Eta$ons.. 2/

c. 7aronic 6eneration 2

. Measurin" Li"#t.. 28a. 3etectors.. 28

%. Caeras39es 28

Appendix1. &I Pre!i:es.. 2

2. Laser C$assi!ications.. 2

). Cornin" &M+;28 *tica$ +i%er Product 3ata s#eet


2/32

Basic Optics

Introduction

In 1/0, t#e !irst Ru%9 $aser 'as %ui$t >1?, oenin" t#e door !or an9 ne' otica$

in5entions and researc# toics. Mec#anica$ en"ineers in articu$ar are current$9 'orkin"on otica$ et#ods !or easurin" !$uid and "as roerties, easurin" ec#anica$

stresses, and anu!acturin" tec#niues. In order to understand t#ese ne' de5e$oents,

a %asic understandin" o! $i"#t and $i"#t roerties is reuired. @#ese notes are eanton$9 as a re5ie' o! $i"#t toics in order to understand rinci$es coon$9 used in t#e

ec#anica$ en"ineer-s otica$ $a%orator9. @#e #9sics %e#ind t#e ateria$s %ein"

resented are "enera$$9 co5ered in introductor9 #9sics courses.

Properties of Light

Aisi%$e $i"#t is a sa$$ art o! t#e e$ectroa"netic sectru. E$ectroa"netic 'a5es

#a5e e$ectric and a"netic !ie$ds erendicu$ar to t#e direction o! otion. @#e9 are a%$e

to tra5e$ t#rou"# a 5acuu or a ediu. @#ere are se5era$ roerties coon$9 used todescri%e $i"#t suc# as co$or B'a5e$en"t#, 'a5enu%er, !reuenc9, ener"9, and o'er

Bintensit9.

Figure 1.1 E$ectroa"netic sectru, #ttD#9er#9sics.#9;astr."su.edu#%asees1.#t$

Wa5e$en"t# BD easured in nanoeters Bn, icroeters B, or an"stros B , 1 0.1 n, t#e distance !ro one eak to t#e ne:t.

+reuenc9 B!D easured in 7ert( B7(, 17( 1s;1. +reuenc9 is t#e in5erse o! t#e tie

it 'ou$d take a 'a5e to tra5e$ 1 'a5e$en"t#. @o ca$cu$ate !reuenc9 !ro 'a5e$en"t#D

fc= B1.1&eed o! $i"#t in a 5acuu Bc ) : 108s

Wa5enu%er BD easured in in5erse centieters Bc;1. @#e 'a5enu%er is #o'

an9 'a5es !it in t#e distance o! 1 c.

2


3/32

Ener"9 BED easured in Fo$e, F#oton, or e$ectron 5o$t BeA, 1eA1./ : 10;1F er

#oton or er o$e o! #otons. Ener"9 o! t#e 'a5e can %e ca$cu$ated direct$9 !ro t#e

'a5e$en"t# or !reuenc9 usin" t#e !o$$o'in" euationD

chhfE == B1.2

P$anck-s constant, h/./2/ : 10;)4

Fs.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"xa#ple 1.1

a. Consider a 10 n 'a5e. W#at are t#e !reuenc9, 'a5enu%er and

ener"9 Bin a 5acuuG

Frequency:

( ) Hz

s

Hz

m

nm

nms

mcf 14

8

10H4.11

1H

10

1H

10

1H

10H)=

==

1$% T&'

Wavenumber:

=

cm

m

m

nm

nm 100

1H

10

1H

10

1

(%)1.(1c#*1

Energy:

( )

==

sxJsxhfE

1104.1H10/2/./ 14)4 1.+,)x1-*1$/photon

%. Consider t#e dia"ra %e$o'. W#at is , , and !G

W#en ca$cu$atin" di!!erences, it is iortant con5ert into coon unitsbeforetakin" t#e di!!erence.

00n;/00n 1--n#

cm

m

m

nm

nmnm 100

1H

10

1H

00

1

/00

1 +0,-.$)c#

*1

)

>n?

P

>W?

/00 00


4/32


5/32

nm

mW.. in

0001.0

1=

=

1- 3/n#

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

Po$ari(ationD W#en t#e e$ectroa"netic 'a5es coosin" a $i"#t %ea 5i%rate in t#esae direction, t#e $i"#t is said to %e o$ari(ed. Po$ari(ed $i"#t is "enera$$9 c$assi!ied into

2 "rous deendin" on #o' t#e e$ectric 'a5es are a$i"ned 'it# t#e $ane o! incidence.

@#e $ane o! incidence is t#e $ane coosin" t#e incident, re!$ected, and transitted

ra9s. @rans5erse a"netic B@M, ara$$e$ BJJ, P, and * are a$$ 'a9s to re!er to 'a5es t#atare o$ari(ed suc# t#at t#e e$ectric !ie$d is in t#e $ane o! incidence. @rans5erse e$ectric

B@E, erendicu$ar B , &, and E are a$$ 'a9s to re!er to o$ari(ation erendicu$ar tot#e $ane o! incidence. @#e o$ari(ation o! $i"#t can a!!ect an9 asects o! otics.Materia$s can #a5e di!!erent roerties !or di!!erent o$ari(ations, suc# as inde:es o!

re!raction B%ire!rin"ents or re!$ecti5it9. In addition to t#ese o$ari(ed cases, $i"#t can %e

rando$9 o$ari(ed Ba$so ca$$ed natura$ $i"#t, or circu$ar$9 or e$$itica$$9 o$ari(ed.

Figure 1.0Para$$e$ o$ari(ation dia"ra.

Figure 1.%Perendicu$ar o$ari(ation dia"ra.

Optical Funda#entals

In t#is section, !undaenta$ otica$ rinci$es 'i$$ %e re5ie'ed in order to understand$i"#t %e#a5ior. *nce t#ese %asic rinci$es are understood, co$e: otica$ a$ications

W#en t#e e$ectric !ie$d

BE is ara$$e$ to t#eaer Bas dra'n, it is

ca$$edD @M, P, *, or JJ.

@#e ara$$e$ $ines are 1

reresentation o! t#iso$ari(ation.

Incident ra9 Re!$ected ra9

@ransitted ra9

W#en t#e e$ectric !ie$dBE is erendicu$ar to

t#e aer $ane, it is

ca$$edD @E, &, E, or .

@#e dots are 1

reresentation o! t#is

o$ari(ation.

Incident ra9 Re!$ected ra9

@ransitted ra9


6/32

and too$s can %e studied. @#ere!ore, it is 5er9 iortant to #a5e a "ood understandin" o!

t#ese !undaenta$ rinci$es.

+erat-s Princi$e

+erat-s rinci$e states t#at $i"#t 'i$$ take at# 'it# t#e s#ortest tra5e$ tie to "o !ro

one oint to anot#er, as s#o'n in !i"ure 4.

Figure 1.) I$$ustration o! +erat-s rinci$e, $i"#t 'i$$ tra5e$ in a strai"#t $ine !ro one oint to anot#er

since a strai"#t $ine 'i$$ %e t#e uickest at#.

+erat-s rinci$e can %e used to s#o' t#e %e#a5ior o! re!$ection. 3eendin" on t#e

incident an"$e o! t#e $i"#t onto a sur!ace Bsa9 a irror, $i"#t 'i$$ on$9 re!$ect at t#at sae

incident an"$e. @#ere!oreD

ri = B1.)

Figure 1.(+erat-s rinci$e on a irror. @#e %ea !ro t#e das#ed at# is iossi%$e %ecause it is a

$on"er tra5e$ tie t#an t#e so$id $ine at#.

+erat-s rinci$e can a$so %e used to s#o' #o' a $ens !ocuses $i"#t. In order tounderstand t#is #enoenon, it is iortant to kno' t#at $i"#t tra5e$s at di!!erent seeds

deendin" on t#e inde: o! re!raction Bn o! t#e ateria$. 6$ass t9ica$$9 #as an inde: o!re!raction o! a%out 1., '#ereas air #as an inde: o! re!raction o! essentia$$9 1 Bc seedo! $i"#t in a 5acuu. @#e seed t#at $i"#t tra5e$s t#rou"# a ediu isD

n

cvlight= B1.4

In !i"ure /, it can t#en %e deduced t#at $i"#t 'i$$ tra5e$ !ro oint = to oint in t#esae aount o! tie Band t#ere!ore t#e s#ortest aount o! tie !or a$$ o! t#e $ines.

BHintD t#e t#ickest art o! t#e $ens #as t#e o5era$$ s#ortest at# $en"t#, %ut since t#e $i"#t

/

2

1

1

2


7/32

'i$$ tra5e$ s$o'er in t#e "$ass, t#e o5era$$ tie to tra5e$ !ro = to 'i$$ %e t#e sae !or

t#e center$ine.

Figure 1. Li"#t at#'a9s t#rou"# a $ens, oint = and are at t'ice t#e !ocus $en"t# o! t#e $ens.

&ne$$-s La'

&ne$$-s $a' redicts t#e direction o! $i"#t as it tra5e$s t#rou"# di!!erent edius. &ne$$-s$a' can %e stated %9 t#e !o$$o'in" euation '#ere nis t#e inde: o! re!raction, and i, t,andrstand !or incident, transitted, and re!$ected.

ttii nn sinsin = B1.

Figure 1.,3ia"ra o! &ne$$-s $a', s#o'in" $i"#t tra5e$in" !ro air to "$ass.

@ota$ interna$ re!$ection can occur '#en $i"#t in a #i"# inde: ediu reac#es a $o'

inde: ediu Bni nt. In t#ese conditions, '#en t0o, t#e corresondin" incident

an"$e is ca$$ed t#e critica$ an"$e. =n9 incident ra9 at t#e critica$ an"$e or #i"#er 'i$$

cause tota$ interna$ re!$ection, eanin" a$$ o! t#e $i"#t is re!$ected and none is transitted.@#is 'i$$ %ecoe iortant '#en dea$in" 'it# !i%er otic ca%$es.

n"$ass

1.

nair

1

r

t

i

=


8/32

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

"xa#ple 1.0

a. Consider a %ea tra5e$in" !ro air Bn1 to "$ass Bn1. at a )0oincident an"$e. &ketc# t#e s9ste, ca$cu$atin" t#e re!$ection and

transission an"$es.

ri = 0-oB+erat-s Princi$e

ttii nn sinsin = B&ne$$-s La'o

iti nn )0L.1L1 ===

( )

= )0sinH

.1

1sin 1t 1$.%

o

%. W#at is t#e critica$ an"$e Bonset o! tota$ interna$ re!$ection !or a"$assair inter!aceG inc;&e$enideair Bn2.G

@o !ind t#e onset o! tota$ interna$ re!$ection B@IR, set t#e transissionan"$e eua$ to 0o. @#ere!oreD

/lass:

( )

=

= 1H

1

.1sin0sinsin 11

i

ti

n

n %1.,o

0inc"1elenide:

( )

=

= 1H

1

.2sin0sinsin 11

i

t

i

n

n +0.),o

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

+resne$-s Euations

@#e aount o! $i"#t t#at is transitted or re!$ected can %e deterined %9 t#e +resne$

euations. @#e ratio o! re!$ected to incident o'er Bor t#e !raction o! o'er re!$ecteddeends on t#e o$ari(ation o! t#e $i"#t, and can %e 'ritten asD

8

n"$ass

1.

nair

1

)0o

1.o

)0o


9/32

2

JJcoscos

coscos

+

=itti

tiit

nn

nn2

BPara$$e$ o$ari(ed $i"#t B1./

2

coscos

coscos

+

=ttii

ttii

nn

nn2

BPerendicu$ar o$ari(ed $i"#t B1.

'#ic# can %e si$i!ied to

2

+

=ti

it

nn

nn2 '#en i0. 2is a$so ca$$ed t#e re!$ected

o'er coe!!icient. I! no $i"#t is a%sor%ed in t#e ateria$, transitted o'er can t#en %e

ca$cu$ated %9 initia$ o'er u$ti$ied %9D

C1B 23 = B1.8!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"xa#ple 1.%

a. I! a 1W $aser %ea is directed t#rou"# a "$ass icroscoe s$ide,'#at is t#e transitted o'erG (4ssume there is no 5o6er absor5tion in

the glass)

Usin" t#e +resne$ euations, it is ossi%$e to ca$cu$ate t#e re!$ected o'er

coe!!icient !or %ot# t#e air"$ass inter!ace, and t#e "$ass air inter!ace. It

turns out t#at t#ese are t#e saeD

04.0.2

.0 22

=

=

+

=ti

it

nn

nn2

&ince t#ere is no a%sor%ance, t#e transitted o'er coe!!icient is t#en Nust1;2. @#ere!ore, /O B1;0.04 o! t#e o'er is transitted, or 0./W.

%. W#at 'ou$d %e t#e transitted o'er i! t#ere 'ere 0 icroscoe

s$ides %et'een t#e $aser and detectorG (4ssume an air ga5 bet6een eachslide)

Rea$i(in" t#at at eac# inter!ace, /O o! t#e o'er is transitted, and t#ereare a tota$ o! 100 inter!aces, it can %e deduced t#atD

01/.0C/.0B 100 ==3@#ere!ore, 1./O o! t#e ori"ina$ o'er or 0.01/W is transitted.

1W $aser

air"$ass inter!ace

"$assair inter!ace

Li"#t detector,

a%$e to easureo'er o! $i"#t

%ea.


10/32

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

Figure 1.$Re!$ection 5ersus incident an"$e !or an air"$ass s9ste.

Euations B1.4 and B1. can %e $otted 5ersus incident an"$e, as s#o'n in !i"ure 1.. =t

/.4o, t#ere is no re!$ection !or one o! t#e o$ari(ations. @#is is a secia$ incident an"$ekno'n as re'ster-s an"$e. 9 aniu$atin" t#e incident an"$e, it is ossi%$e to o$ari(e

uno$ari(ed $i"#t.

"xa#ple 1.)

I! t#ere 'ere t#e sae 0 s$ides as in e:a$e 1.), %ut no' t#e incident

an"$e 'as at re'ster-s an"$e, '#at 'ou$d t#e transitted o'er %eG

(4ssume the light is un5olarized* and equal amounts of 5er5endicular and5arallel"5olarized light)

4ns6er:

=t re'ster-s an"$e, none o! t#e ara$$e$;o$ari(ed $i"#t 'i$$ %e re!$ectedB100O transission, or 0O net transission. +ro euation Bor !ro

t#e "ra# in !i"ure 8, t#e re!$ection !or 1 air"$ass and "$assair 0.14.

@#ere!ore, t#e erendicu$ar o$ari(ed $i"#t transits 8.1O B1;0.14 ateac# inter!ace, so o5er a$$ 100 inter!aces, 0.81100.84:10;8is transitted

Bessentially !.

*5era$$, t#e tota$ transission is t#en )-4.

Etendue

Etendue, a$so kno'n as t#e araeter roduct, can %e t#ou"#t o! as t#e ua$it9 o! $i"#t,and is uanti!ied %9 si(e u$ti$ied %9 di5er"ence. @#e sa$$er t#e etendue, t#e %etter

co$$iated t#e $i"#t can %e. Etendue is t#e otica$ eui5a$ent o! entro9 at %est it 'i$$

10

Reflection versus incident angle (air-glass interface)

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

Incident Angle

Reflectance

RJJ

R

re'ster-san"$e/.4o


11/32

reain constant, #o'e5er it 'i$$ ne5er iro5e. +i"ure 1.10 s#o's #o' etendue is

ca$cu$ated and "ra#ica$$9 reresented.

Figure 1.1- 6ra#ica$ reresentation o! etendue.

@#e sa$$est etendue ossi%$e is ca$$ed t#e di!!raction $iit. @#e di!!raction $iit is

'a5e$en"t# deendent, and can %e ca$cu$ated !ro t#e !o$$o'in" euation, '#ere dis t#e

sot si(eQ, t#e diaeter o! t#e $i"#t sourceD

( )

halfdH B1.8

@#e di!!raction $iit t#ere!ore $eads to t#e iniu sot si(e t#at a %ea cou$d roduce

Brat#er t#an an in!inite$9 sa$$ oint. Lasers are a%$e to roduce $i"#t t#at is neardi!!raction $iited. = "enuine increase in etendue is ca$$ed %ea steerin".

"xa#ple 1.(

a. Li"#t at /10 n, $ea5es a $aser at t#e di!!raction $iit. @#e$aser #as a 1 diaeter eittin" area. W#at is t#e di5er"ence

an"$e o! t#e $aserG

=halfdH

=

m

m

nm

m

m

nmhalf

1

10H

10

1H

1

1H

/10 /

11.1+)o

%. I! t#e $aser %ea 'ere co$$ected in a 1 c diaeter $ens at t#e !oca$$en"t#, #o' $ar"e 'ou$d t#e roNected sot %e 10 k !ro t#e $ensG

First* calculated the divergence angle leaving the lens:

( ) ( )2211 sinsin rr =

mmr

.02

11 =

=

11

!

a1

1

2

2

Etendue %est caseD

a1sinB

1a

2sinB

2

1tan;1Ba

2!

2tan;1Ba

1!

Li"#t source

a2


12/32

cmr

o

.0

2.22

2

1

=

=

( )

=

=

m

cm

m

m

cm

m

r

r o

1

100H

10

1H

.0

2.22sinH.0sin

CsinBsin

/

1

2

1112

0.002o

Next* using trigonometry* figure outthe size of the s5ot:

( ) ( )o7r 002.0tanH10000tanH 2) == 0.) 2

)H r4 = -.%) #+

Co#erence

W#en 2 or ore $i"#t %eas are sueriosed on eac# ot#er, t#e9 #a5e t#e otentia$ to%e eit#er co#erent or inco#erent. W#en co#erent $i"#t #as t#e sae eaks and 5a$$e9s, it

constructi5e$9 inter!eres, '#ereas i! a eak $ines u 'it# a 5a$$e9, t#ere is destructi5e

inter!erence, '#ic# 'eakens t#e si"na$.

W#en 'a5es o! di!!erent 'a5e$en"t#s are tra5e$in" a$on" t#e sae at#, it is use!u$ tokno' at '#at $en"t# t#e 'a5es %ecoe inco#erent. @#is co#erence $en"t#- can %e

ca$cu$ated 'it# t#e !o$$o'in" euationD

=

2

c7 B1.

12

Destructive Interference

-1.5

0

1.5

0

Constructive Interference

-2

0

2

0 250

Incoherent Light

-1.2

0

1.2

0

Figure 1.11E:a$es o! destructi5e and constructi5e

inter!erence, and inco#erent $i"#t.


13/32

"xa#ple 1.

@'o 10 W $asers eittin" 5er9 near$9 t#e sae co$or are arran"ed ass#o'n %e$o'. @#e to $aser is a !ree;runnin" $aser, and t#e %otto is a

sta%i$i(ed $aser t#e sta%i$i(ed $aser #as a si"ni!icant$9 sa$$er $ine'idt#.

@#e !u$$ 'idt# #a$! a:- B+W7M o! t#e to $aser is 0.1 c;1

, and t#e+W7M o! t#e $o'er $aser is )00 k7(. +W7M is t#e %and'idt# at #a$! t#ea:iu, since ost $asers and ot#er otica$ sources roduce 'a5es on a

6aussian cur5e +W7M is a "ood aro:iation o! %and'idt#.

+ree runnin" $aserD fr 00.01 n, +W7M 0.1c;1

&ta%i$i(ed $aserD s 00 n, +W7M )00 k7(

a. W#at is t#e co#erence $en"t# o! t#e 2 $asersG

Free running laser:

+

=

frfrfrfr

fr

nm

m

m

cmcm

H.0

1

H.0

1

10

1H

1

100H

1

fr 0.004 n

nm

m

nm

nm7 frc

222

,10

1H

004.0

01.00=

=

-.1 #

1tabilized laser:

+

=

ssss

cHz

Hz8Hz

H.0

1

H.0

1H

1

1000H

s4.:10;n

nm

m

nmx

nm7

s

s

sc

222

,10

1H

10.4

00

=

=

15--- #

%. @#e detector is not readin" a si"na$. W#9 cou$d t#is %eG

4ns6er:

1)

+ree runnin"

sta%a$i(ed

3etectorLasersD

%ea s$itter

irror

)0 c


14/32

&ince t#e co#erence $en"t# in t#e !ree;runnin" $aser is s#orter t#an t#e at#

it is tra5e$in", t#e $i"#t %ecoes inco#erent, and t#ere!ore cannot a$i"n

'it# t#e sta%i$i(ed $aser.

&catterin"W#en $i"#t #its o$ecu$es, it can %ecoe scattered in se5era$ 'a9s. W#en $i"#t is

scattered %9 5er9 sa$$ o$ecu$es Bd SS e$astic BRa9$ei"# scatterin", ine$astic 'it#

increased ener"9 B=nti;&tokes Raan scatterin", or ine$astic 'it# decreased ener"9

B&tokes Raan scatterin" scatterin" can occur. W#en $i"#t is scattered %9 $ar"er

o$ecu$es Bd, Mie scatterin" occurs.

@#e incident o'er, densit9 o! o$ecu$es, 5o$ue o! interest, and co$$ection an"$e o! t#e

otics can deterine t#e scattered o'er !or eac# t9e o! scatterin". @#e euation !or

scattered o'er is as !o$$o'sD

=

n7.

.

9

s

B1.10

9

s

.

. ratio o! scattered o'er to incident o'er

di!!erentia$ scatterin" cross;section

&rHo$ecu$es

c2

so$id an"$e o! co$$ection >&r?, 1 &teradian 4Hradians

n o$ecu$ar densit9

(at standard tem5erature and 5ressure* air has a molecular density of:

#&+!

'

molecules;cm

$

)2ayleigh:

42

22 C1B4

o2ayleigh N

n=

B1.11

13.nmatN2ayleigh 1rmolec

cm

,00

2

28

2

10H4.8

!or en. B1.11, n re!racti5e inde: o! o$ecu$e

No nu%er densit9 at &@P

@#is in5erse re$ations#i 'it# 'a5e$en"t# can %e used to e:$ain '#9 durin" t#e da9, t#e

sk9 is %$ue and not red. =s t#e sun sets, t#e sun-s ra9s tra5e$ t#rou"# ore o! t#eatos#ere, a$$o'in" ore scatterin", causin" t#e sunset to %e a redder co$or.

2aman:

2ayleigh2aman

)10

-ie:

14


15/32

2

2d-ie

=

d diaeter o! scatterin" o$ecu$e

Wa5e$en"t# c#an"es due to Raan scatterin" can %e ca$cu$ated %9 t#e !o$$o'in"euationsD

=nti;&tokes RaanDhEEE +=+ TL B1.12

&tokes RaanDh

EEE

= TL B1.1)

"xa#ple 1.,

= 1 W $aser at 00n is directed into air at roo teerature and

ressure. I! a detector cou$d ick u 10O o! t#e area o! a s#ere, and 1 c$on", #o' uc# o'er 'ou$d %e detected due to Ra9$ei"# scatterin"G

4ns6er:

=

2ayleigh9

s n7

.

.

n2.H101o$ecu$esc)

0.1H4 1.2/

71 c

=

1rmolecule

cmx

2ayleigh H104.8

228

.s 2.8/:10;8W

Conclusions

In t#is section, 'e #a5e de5e$oed t#e too$s necessar9 to understand #enoena dea$in"'it# otics. Wit# t#ese !undaenta$ rinci$es, 'e can no' o5e a#ead to $earnin"a%out t#e instruents used in otica$ $a%oratories, and ot#er otica$ a$ications.

1

L

Pin

3etector


16/32

Optical Laboratory Toolbox

In t#e otica$ $a%orator9, it is iortant to %e a%$e to contro$ t#e direction, 'a5e$en"t#,

and sectra$ o'er o! $i"#t. Usin" t#e rinci$es de5e$oed in t#e re5ious section, it is

ossi%$e to do t#is in an9 'a9s. Lasers and LE3s can %e used to create $i"#t at seci!ic'a5e$en"t#s and o'ers. Lenses, irrors, and !i%er otics can %e used to direct $i"#t.

3i!!raction "ratin"s and eta$ons are e:a$es o! 'a9s to contro$ t#e 'a5e$en"t#. +ina$$9,

5arious detectors can %e used to easure $i"#t roerties.

Creating Light

W#en 'e t#ink o! arti!icia$ $i"#t sources, t#e !irst t#in" t#at coes to ind is ro%a%$9 a$i"#t %u$%. Li"#t %u$%s "i5e o!! inco#erent $i"#t o5er a 'ide ran"e o! 'a5e$en"t#s.

7eatin" eta$ !i$aents creates $i"#t in standard $i"#t %u$%s. W#en seci!ic 'a5e$en"t#s

or co#erent $i"#t is reuired, $asers or LE3-s are t#e usua$ et#od.

Lasers 7i"#t4$i!ication %9 1tiu$atedEission o!2adiationLasers roduce co#erent e$ectroa"netic 'a5es at narro' 'a5e$en"t# %ands, eit#er

continuous$9 or u$sed. @#ere are t#ree arts to a $aserD "ain ediu, u, and!eed%ack. @#e %asic idea %e#ind a $aser is t#at !irst atos in t#e "ain ediu are e:cited

to #i"#er t#an usua$ ener"9 states. *nce enou"# atos are e:cited, a #oton causes t#e

to dro to a $o'er ener"9 state. In "oin" !ro a #i"#er ener"9 state to a $o'er ener"9state, t#e atos "i5e o!! anot#er #oton at a seci!ic 'a5e$en"t#. @#ese #otons cascade

t#rou"#out t#e ediu %et'een irrors, causin" ore t#e rocess to continua$$9 reeat.

+ina$$9, one o! t#e irrors 'i$$ #a5e on$9 artia$ re!$ection, a$$o'in" a %ea to e:it t#e

ca5it9 Bsee !i"ure 2.1. Lasers #a5e t#e otentia$ to #a5e 5er9 #i"# o'er, and cou$d %edan"erous i! roer sa!et9 recautions are not used. =endi: ) %reaks do'n t#e t9es

o! $asers into c$assi!ications %ased on o'er and otentia$ #ar!u$ness.

Figure +.1 &i$i!ied dia"ra o! a Ru%9 $aser. Ru%9 B=$2*) Cr is t#e "ain ediu $as are used to

u t#e ru%9 to an e:cited state 'it# irrors on eit#er end o! t#e ca5it9.

Lasers are c$assi!ied accordin" to t#e ediu t#at is %ein" e:cited. @#e t#ree %asic

cate"ories are so$id Bi&e&Ru%9, "as Bi&e&7e;


17/32

deterines t#e 'a5e$en"t# t#at t#e $aser roduces. 6ain edius can %e 5er9 di!!erent,

%ut essentia$$9 t#e9 a$$ need to do t#e sae t#in". +irst, a ou$ation in5ersionQ needs to

occur. Indi5idua$ atos nora$$9 are !ound in a "round ener"9 state. W#en 1 e$ectron ise:cited and o5es to a di!!erent or%itin" s#e$$, t#e ato #as an o5era$$ #i"#er ener"9

state. Pou$ation in5ersion occurs '#en t#ere are ore atos in t#e e:cited state t#an t#e

"round state. =n e:a$e o! a no%$e "as B


18/32

Figure +.%@#e t#ree ain transitions, stiu$ated a%sor%ance, sontaneous eission, and stiu$ated

eission.

&oe atos #a5e etasta%$e states, '#ic# are sta%$e, #i"#;ener"9 states. Metasta%$estates are crucia$ !or $asers %ecause t#e9 a$$o's !or ou$ation in5ersion. 6ain edia is

$iited to o$ecu$es t#at #a5e etasta%$e states B"enera$$9 a rare occurrence. =s an

ato "oes !ro t#e etasta%$e state to a $o'er state, it re$eases a #oton 'it# seci!ic'a5e$en"t#. @#ere a9 %e a sa$$ ran"e o! ener"ies at t#e etasta%$e state t#at cause t#e

$aser to #a5e a ran"e o! 'a5e$en"t#s. 3eendin" on t#e a$ication, t#is can %e eit#er

%ene!icia$ or not. We 'i$$ see $ater in t#is c#ater #o' to aniu$ate 'a5e$en"t#s.

Pro%a%$9 t#e %est 'a9 to understand #o' $asers 'ork is to $ook at an aniation !ro oneo! t#e 'e%sites $isted in aendi: 4, #o'e5er !i"ure 2. "i5es a "enera$ o5er5ie' o! t#e

rocess. = $ist o! soe a5ai$a%$e $asers and t#eir 'a5e$en"t#s is $isted in aendi: 2.

18

&ontaneous Eission

#oton

6round &tate

E:cited &tate

&tiu$ated Eission

6round &tate

E:cited &tate

Ener"9@ransissions


19/32

Figure +.) &tes in creatin" a $aser. @#e "ra9 dots reresent atos as t#e9 tra5e$ !ro natura$$9 occurrin"

"round states, to #i"#er etasta%$e states '#en stiu$ated %9 #otons. @#is !i"ure is si$i!ied !or c$arit9.

In actua$it9, eac# ato %ein" stiu$ated reuires 1 #oton, '#ereas on$9 1 #oton tota$ is s#o'n in t#is

dia"ra. @#e #otons %ounce %ack and !ort# %et'een t#e surroundin" irrors Bnot s#o'n, a$$o'in" t#e

stiu$ated eission to continue. @#e odd ato t#at 'ent to a #i"#er state is a rare occurrence it is s#o'n#ere to si$9 to i$$ustration '#at can #aen.

=s entioned %e!ore, $asers can %e eit#er u$sed or continuous. Pu$sed $asers #a5e a

$iit to #o' s#ort t#e9 can %e %ased on t#e 7eisen%er" Uncertaint9 Princi$e, '#ic# is

stated as !o$$o'sD

4hEt B2.1

'#ere tis t#e u$se duration, Eis t#e ener"9 Bree%erE


20/32

11 0010.0.1//// +=+ cmcm 1////.010 c;1

=

+=

010.1////

1

.1////

111

0.0000)8 n

==

nm

m7c

22

10

1

0000)8.0

/00

$.) #

@#e $en"t# o! t#e u$se is Nust seed o! sound u$ti$ied %9 t#e u$se durationD

[ ] [ ]

==

ns

sns

smxtc7 55ulse

8

10

1H10H10)H 0 #

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

LE3s 7i"#tEittin"=iodes

LE3s are sii$ar to $asers, #o'e5er t#e9 use on$9 sontaneous eission rat#er t#an

stiu$ated. Reo5in" t#e irrors !ro a $aser "ets rid o! t#e stiu$ated eission. @#e

ain di!!erence t#ere!ore %et'een $asers and LE3s is t#at LE3s roduce inco#erent$i"#t. &ince LE3s are ore e!!icient t#an $i"#t %u$%s, and $ess #ar!u$ to t#e #uan e9e

t#en $asers, LE3s #a5e !ound an9 ractica$ a$ications suc# as %rake $i"#ts and sto

$i"#ts.

6irecting Light

*nce 'e #a5e $i"#t !ro a $i"#t source, 'e need to %e a%$e to accurate$9 contro$ '#ere ittra5e$s. @#ere are se5era$ 'a9s to do t#is. Lenses can %e used to co$$iate or !ocus $i"#t.

Mirrors are used to re!$ect $i"#t. +ina$$9, !i%er otic ca%$es are 5er9 use!u$ !or

trans!errin" $i"#t to seci!ic $ocations.

LensesLenses can %e used to eit#er !ocus or co$$iate $i"#t. = $ens can %e conca5e, con5e:, or

co%inations o! t#e 2. Co$$iated $i"#t coin" in t#rou"# a conca5e $ens 'i$$ !ocus att#e !oca$ $en"t# Bf. In "enera$, t#e 6aussian $ens !oru$a isD

=+fss io

111B2.)

and t#e a"ni!ication !ro t#e $ens isD

o

i

s

s-= B2.4

20


21/32

Figure +.(3ia"ra !or 6aussian $ens !oru$aD B1so B1si B1!

Figure +. Lens secia$ case, a oint source at t#e !oca$ $en"t# co$$iates $i"#t. = oint source not on t#ecenter $ane B9et sti$$ at t#e !oca$ $en"t# 'i$$ co$$iate t#e $i"#t at an an"$e to t#e center $ane.

Figure +.,=n ia"e at t'ice t#e !oca$ $en"t# 'i$$ "i5e 1D1 ia"in".

@#e +;nu%er Bre!erred to asD +V or +V in industr9 o! a $ens isf;d, as s#o'n in !i"ure2.8. *t#er %e#a5iors o! $enses can %e deterined !ro &ne$$-s $a'. =na$9tica$$9, t#is can

21

f

2f

;2f "f f

d

so

si

i;con5e: $ens


22/32

%e uite ri"orous, #o'e5er "ra#ica$ so$utions or ra9 tracin" so!t'are ro"ras can

si$i!9 t#e coutationa$ 'ork.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"xa#ple +.+

6i5en an LE3 'it# a 100 diaeter eission area, and #a$!;an"$e di5er"ence

o! 20o, '#at +V $ens 'ou$d 9ou need to #a5e a di5er"ence #a$! an"$e o! a t9ica$$aser ointer, 0.01oG

4ns6er:+irst ca$cu$ate t#e iniu diaeter o! t#e $ens !ro %asic etendue rinci$esD

=

21,22

21,11 sinsin dd

( )( )01.0sin

20sin10100

sin

sin /

2

1,2

21,11

2

ox

d

d

=

=

0.1/


23/32

%$urrin" o! t#e ia"e 'i$$ resu$t, '#ic# is kno'n as coa a%erration. +ie$d cur5ature

occurs '#en a $ens tends to !ocus on a cur5ed, rat#er t#an !$at $ane. W#en ia"e s#aes

do not actua$$9 corre$ate 'it# t#e actua$ s#ae o! t#e o%Nect, distortion is occurrin".3istortion is usua$$9 increased as t#e o%Nect is $aced !urt#er o!! t#e center a:is. +ina$$9,

c#roatic a%erration occurs '#en di!!erent 'a5e$en"t#s #a5e di!!erent %e#a5iors t#rou"#

t#e $ens, causin" di!!erent co$ors to !ocus at di!!erent oints. It is iortant to kno' t#ata$$ o! t#ese a%errations can %e eit#er e$iinated or inii(ed 'it# 5arious tec#niues

suc# as usin" u$ti$e $enses or t#e use o! as#erica$ irrors.

Mirrors

Mirrors are ade 'it# #i"#$9 re!$ecti5e sur!aces. +erat-s rinci$e can %e used to

deduce t#at t#e re!$ection an"$e is a$'a9s eua$ to t#e incident an"$e. =side !ro !$at

irrors, ara%o$ic s#aed irrors are coon$9 !ound in otica$ $a%oratories. Para%o$icirrors !ocus $i"#t to a oint.

+i%ers

= 5er9 use!u$ too$ in toda9-s otica$ too$%o: is t#e !i%er. +i%ers are essentia$$9 dra'n"$ass Bor soe transarent ediu 'it# a rotecti5e coatin". = sa$e dia"ra o! a

!i%er is "i5en in !i"ure 2..

Figure +.$ 3ia"ra o! !i%er otic ca%$e.

W#en $i"#t is directed into t#e core at sa$$ enou"# an"$es, tota$ interna$ re!$ection 'i$$

occur %et'een t#e core and c$addin" inter!ace. @#e nuerica$ aerture is t#e sine o! t#ea:iu #a$! an"$e t#at can %e directed at t#e core and tota$ interna$ re!$ection 'i$$ sti$$

occur Bsee !i"ure 2.10. @#e !o$$o'in" euation can t#ere!ore %e ca$cu$ated !ro &ne$$-$a'D

22

21sin claddingcore nnN4 =

= B2.

2)

Core, n1

C$addin", n2

u!!er

Facket


24/32

Figure +.1- W#en $i"#t is "uided into a !i%er at an an"$e $ess t#en t#e #a$! an"$e, tota$ interna$ re!$ection

'i$$ occur, iro5in" $i"#t transission.

W#en t#e diaeter o! t#e !i%er core is sa$$ enou"#, 'a5es on$9 can tra5e$ in one at#.

@#ese !i%ers are ca$$ed sin"$e;ode !i%ers. =t $ar"er diaeters, 'a5es coin" in at

di!!erent an"$es can tra5e$ in di!!erent at#s, and are t#ere!ore tered u$ti;ode at#s.@#e nu%er o! odes a !i%er #as can %e deterined !roD

V odes 2

.0

=

dN4Nm B2./

3ue to t#e "enera$$9 $on" $en"t#s, attenuation B$oss due to scatterin" and a%sor%ance is acritica$ roert9 !or !i%ers. +i"ure 2.11 s#o's attenuations in deci%e$s er ki$oeter !or a

coon !i%er ateria$, si$ica. Po'er transission !or t#e $en"t# o! !i%er can %e t#en

ca$cu$ated.

10107

3

= B2.

'#ere is t#e $oss in deci%e$s er $en"t#Bdk, and 3is o'er out o5er initia$ o'er.

=endi: 4 is a roduct data s#eet !or Cornin"-s &M+;28 *tica$ +i%er B&M+ sin"$eode !i%er. 7oe!u$$9 %9 no' ost o! t#e roerties are c$ear.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"xa#ple +.%

Usin" !i"ure 2.11, '#at is t#e transission Bratio o! outut to inut intensit9 o! a

10 k $en"t# o! !i%er at 80 nG =t 10 nG

4ns6er:+ro t#e !i"ure, at 80 n, t#ere is aro:iate$9 2 dk attenuation $oss,

10

10H2

80 10

=nm3 14 transission

at 10n t#ere is aro:iate$9 0.2 dk attenuation $oss

24

Core, n1.

C$addin", n1.48

Li"#t 'it#in t#is cone

is "uided a$on" !i%er

cr

12

12

12.2o

12


25/32

10

10H2.0

10 10

=nm3 (0 4transission

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

Figure +.11 =ttenuation in !used si$ica Bcoon ateria$ o! !i%ers. +roD

#ttD'''.se.onas#.edu.auteac#in"sc)011e$ecXotB).d!Bro%a%$9 s#ou$d !ind a %etter "ra#

Controlling 3a7elength

Man9 ties, it is necessar9 to 'ork 'it# a seci!ic 'a5e$en"t# or to searate $i"#t %9

'a5e$en"t#. @#is is esecia$$9 use!u$ in sectrosco9 a$ications. @#ere arean9 'a9s to searate 'a5e$en"t#. @#is section 'i$$ descri%e soe o! t#e

ore strai"#t!or'ard et#odsD di!!raction "ratin"s, eta$ons, and #aronic

"eneration.

3i!!raction 6ratin"

W#en o$9c#roatic $i"#t is directed at a di!!raction "ratin", it is re!$ected as a s#eet.

@#e 'a5es sread out into t#e s#eet accordin" to 'a5e$en"t#. 3i!!raction "ratin"s areirrors 'it# 5er9 recise "roo5es cut into t#e. +i"ure 2.12 i$$ustrates t#e %e#a5ior o! a

di!!raction "ratin".

2
http://www.spme.monash.edu.au/teaching/msc3011/elec_&_opt(3).pdfhttp://www.spme.monash.edu.au/teaching/msc3011/elec_&_opt(3).pdf


26/32

Figure +.1+ 3ia"ra o! a di!!raction "ratin". @#e $i"#t is incident at an"$e , and $ea5es at discreet

an"$es .

@#e "ratin" euation is as !o$$o's, '#ere mis t#e orderD( ) sinsindm += B2.8

&o !or di!!erent 'a5e$en"t#s, t#ere are di!!erent an"$es, causin" t#e $i"#t s#eet. =s a

"enera$ ru$e o! t#u%, t#e ost e!!icient use o! t#e "ratin" occurs around t#e %$a(e

'a5e$en"t#.

+orD efficient>?laze?laze 0

2

)

)

2>

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"xa#ple +.)

=n in!rared B1. diode $aser #as an eittin" area o! 1 : 1 eittin"

area. = !oca$ $en"t# $ens is used to co$$iate t#e $aser. @#e %ea isdirected at a 1200 " B"ratin" er i$$ieter "ratin". =t '#at an"$e does t#e

1storder di!!racted %ea coe %ack to'ards t#e $aser Bt#is is ca$$ed t#e Littro'

an"$eG4ns6er:

+irst, ca$cu$ate dD

[ ] mx&m

mmmm

gd 10))8

10001

12001 =

=

@#en, $u" into t#e "ratin" euationD( ) sinsin +=dm

kno'in"D = !or Littro' condition, and 1 Border 1 sin2= 2 (%.1(o

2/

%$a(e

incident an"$e

re!$ected an"$e

&u%scrits are t#e

order o! t#e "ratin"

d

o

;1

1


27/32

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

Eta$ons

=n eta$on can occur '#ene5er t#ere are airs o! !$at $ates searated %9 an otica$$9

contacted sacer Bsuc# as a $aser ca5it9, or e5en Nust a icroscoe s$ide. 3ue toconstructi5e and destructi5e inter!erence, eta$ons on$9 a$$o' certain 'a5e$en"t#s to %e

transitted. Man9 ties eta$ons are un'anted, #o'e5er eit#er usin" an"$ed sur!aces or

s#i!tin" t#e incident $i"#t to an an"$e can e$iinate t#e.

+ree &ectra$ Ran"e B+&R [ ]Hznd

c

2B2.

n inde: o! re!raction, d distance %et'een ara$$e$ $anes

+inesse B+ 2

2

1

B2.10

and'idt# +W7M B!u$$ 'idt# #a$! a: F

F12B2.11

Figure +.10 Eta$on dia"ra.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"xa#ple +.(

W#at is t#e !ree sectra$ ran"e and +W7M o! a "$ass Bn1. icroscoe s$ide, 1

'ideG

4ns6er:

/101H.1H2 =

x

cF12 100 @7(

[ ]s

x

smx

fcfc

110100

10)

12

8

=== 0# 2 F89

2

+W7M

+&R

Wa5e$en"t#

@ransission

BO


28/32

2

1

1

+

=n

n2 0.04

2

2F

=

1

0./4

[ ]

/4.0

)mm

F

F12

FWH- == %.),% #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

7aronic 6eneration

=side !ro searatin" 'a5e$en"t#s 'it# "ratin"s or usin" inter!erence as in eta$ons, it isossi%$e to i: 'a5e$en"t#s to "et ne' 'a5e$en"t#s. @#ese rocesses ust satis!9

ener"9 and oentu conser5ation B#o'e5er, not #oton conser5ation. +i"ure 2.14

deonstrations #o' di!!erentia$ and suation i:in" can occur.

Figure +.1% I$$ustration o! 2ndand )rd#aronic "eneration.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!"xa#ple +.

+ourt# #aronic "eneration is i$$ustrated in t#e !i"ure %e$o'. Ca$cu$ate t#e !ina$

'a5e$en"t# %9 er!orin" an ener"9 %a$ance. =$$ o! t#e inut %eas enter at10/4 n.

28

non$inear

cr9sta$Q

110/4 n

210/4 n

) )2 n

Ener"9 a$anceDE

in E

out

&econd 7aronic 6enerationD

110/4 n

210/4 n

) )2 n

Ener"9 a$anceD

Ein Eout

)21

hchchc=+

4)

hchchc=+

@#ird 7aronic 6enerationD

410/4 n ) n

non$inearcr9sta$Q


29/32

4ns6er:

+irst, rea$i(e t#e das#ed $ine a%o5e can de!ine t#e s9ste. @#en, EinEoutD

out

hchc

=

1

4

out2 +(( n#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

:easuring Light

*nce 'e !ina$$9 #a5e $i"#t directed in t#e correct direction and at t#e desired 'a5e$en"t#,

it is usua$$9 iortant to %e a%$e to detect t#e $i"#t. Caeras can %e used !or 5isua$detection, and 5arious ot#er detectors can %e used to easure o'er, 'a5e$en"t#,

o$ari(ation, and co#erence. @#is section needs ore 'ork

Conclusion

In t#is section, 'e #a5e %een introduced to soe o! t#e %asic too$s used in an otics

$a%orator9. Li"#t %u$%s, $asers, and diodes can %e used to create $i"#t, irrors, $enses,

and !i%ers can %e used to direct $i"#t. 6ratin"s, eta$ons, and #aronic "eneration are

'a9s to aniu$ate t#e 'a5e$en"t#. +ina$$9, detectors and caeras are used to easure$i"#t intensit9. 9 no 'a9 #o'e5er did t#is c#ater contain a co$ete $ist o! otica$

too$s a5ai$a%$e. In t#e ne:t section, otica$ a$ications 'i$$ %e discussed to rea$i(e t#eotentia$ o! t#ese too$s.

2


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Appendix 1

&cienti!ic Units*tics !reuent$9 dea$s 'it# 5er9 $ar"e or 5er9 sa$$ nu%ers Bn, 67(, etc..

@#ere!ore, it is iortant to %ecoe !ai$iar 'it# t#e &I re!i:esD

@era @ 1012 Centi c 10;2 Pico 10;12

6i"a 6 10 Mi$$i M 10;) +eto ! 10;1

Me"a M 10/ Micro 10;/ =tto = 10;18

Ki$o k 10)


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7ere is anot#er descrition t#at re$ates t#e $aser c$assi!ications to coon $aser t9es and o'er $e5e$sD

C$ass I ; EYEMP@ L=&ER&, considered Tsa!eT !or intra%ea 5ie'in". Aisi%$e %ea.

Ma:iu o'er $ess t#an 0.4 W. @#is 'i$$ not cause daa"e e5en '#ere t#e entire

%ea enters t#e e9e and it is %ein" stared at continuous$9.

C$ass II ; L*W;P*WERE3 AI&ILE BCW *R 7I67 PUL&E R=@E L=&ER&, 'onTt

daa"e 9our e9e i! 5ie'ed oentari$9. Aisi%$e %ea.

Ma:iu o'er $ess t#an 1 W !or 7e


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Appendix % ; =seful 3ebsites

#ttDscience'or$d.'o$!ra.co#9sicstoics*tics.#t$#ttDicro.a"net.!su.edurier$i"#tandco$orinde:.#t$

#ttD'''.#o'stu!!'orks.co

#ttD'e%#9sics.#.sstate.eduNa5airror
http://scienceworld.wolfram.com/physics/topics/Optics.htmlhttp://www.howstuffworks.com/http://webphysics.ph.msstate.edu/javamirror/http://scienceworld.wolfram.com/physics/topics/Optics.htmlhttp://www.howstuffworks.com/http://webphysics.ph.msstate.edu/javamirror/

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