PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

2

light

as

wav

es

so fa

r, lig

ht h

as b

een

treat

ed a

s if

it tra

vels

in s

traig

ht li

nes

ray

diag

ram

sre

fract

ion

To d

escr

ibe

man

y op

tical

phe

nom

ena,

we

have

to tr

eat

light

as

wav

es.

Just

like

wav

es in

wat

er, o

r sou

ndw

aves

, lig

ht w

aves

can

inte

ract

and

form

inte

rfere

nce

patte

rns.

rem

embe

r c=f

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

3

inte

rfere

nce

cons

truc

tive

inte

rfer

ence

de

stru

ctiv

e in

terf

eren

ce

at a

ny p

oint

in ti

me

one

can

cons

truct

the

tota

l am

plitu

deby

add

ing

the

indi

vidu

al c

ompo

nent

s

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

4

Inte

rfere

nce

III

cons

truc

tive

inte

rfer

ence

wave

s in

pha

se

dem

o: in

terf

eren

ce

+ =

dest

ruct

ive

inte

rfer

ence

wave

s ½

out

of p

hase

+ =

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

5

Inte

rfere

nce

in s

pher

ical

wav

esm

axim

um o

f wa

ve

min

imum

of

wave

posi

tive

con

stru

ctiv

e in

terf

eren

cene

gati

ve c

onst

ruct

ive

inte

rfer

ence

dest

ruct

ive

inte

rfer

ence

if r

2-r 1

=nth

en c

onst

ruct

ive

inte

rfer

ence

occ

urs

if r

2-r 1

=(n+

½)th

e de

stru

ctiv

e in

terf

eren

ce o

ccur

s

r 1r 2

r 1=r

2

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

6

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

7

light

as

wav

es

it w

orks

the

sam

e as

wat

er a

nd s

ound

!

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

8

doub

le s

lit e

xper

imen

t•t

he li

ght f

rom

the

two

sour

ces

is in

cohe

rent

(fi

xed

phas

e w

ith

resp

ect t

o ea

ch o

ther

•in

this

case

, the

re is

no p

hase

shi

ft be

twee

n th

e tw

o so

urce

s

•the

two

sour

ces

of li

ght

mus

t hav

e id

entic

al

wav

e le

ngth

s

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

9

Youn

g’s

inte

rfere

nce

expe

rimen

t

ther

e is

a pa

th d

iffer

ence

: dep

endi

ng o

n its

size

the

wav

esco

min

g fro

m S

1or

S2

are

in o

r out

of p

hase

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

10

Youn

g’s i

nter

fere

nce

expe

rimen

t

If th

e di

ffere

nce

in d

istan

ce b

etw

een

the

scre

en a

nd e

ach

of th

e tw

o sli

ts is

suc

h th

at th

e w

aves

are

in p

hase

, con

stru

ctiv

ein

terfe

renc

eoc

curs

: brig

ht s

pot d

iffer

ence

in

dist

ance

mus

t be

a in

tege

r mul

tiple

of

the

wav

elen

gth:

dsin

=m, m

=0,1

,2,3

…

m=0

: zer

oth

orde

r m=1

: firs

t ord

er e

tc

if th

e di

ffere

nce

in d

istan

ce is

off

by h

alf a

w

avel

engt

h (o

r one

and

a h

alf e

tc),

dest

ruct

ive

inte

rfere

nce

occu

rs(d

sin=[

m+1

/2]

, m=0

,1,2

,3…

)pa

th d

iffer

ence

dem

o

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

11

dist

ance

bet

wee

n br

ight

spo

ts

ifis

smal

l, th

en s

inta

nso

:dsin

=m, m

=0,1

,2,3

…co

nver

ts to

dy/L

=mdi

ffere

nce

betw

een

max

imum

m a

nd m

axim

um m

+1:

y m+1

-ym

= (m

+1)

L/d-

mL/

d=L/

dy m

=mL/

d

tan

=y/L

L

dem

o

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

16

othe

r way

s of

cau

sing

inte

rfere

nce

rem

embe

r

equi

vale

nt to

: 12

n 1n

2

12

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

17

phas

e ch

ange

s at

bou

ndar

ies

If a

light

ray

trave

ls fro

m m

ediu

m 1

to m

ediu

m 2

with

n1<

n 2,

the

phas

e of

the

light

ray

will

cha

nge

by 1

/2. T

his

will

not

ha

ppen

if n

1>n 2

. 12

n 1n

2

12

noph

ase

chan

geIn

a m

ediu

m w

ith in

dex

of re

fract

ion

n, th

e w

avel

engt

hch

ange

s (re

lativ

e to

vac

uum

) to

/n

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

18

thin

film

inte

rfere

nce

n=1 n

=1.5

n=1

The

two

refle

cted

rays

can

inte

rfere

. To

anal

yze

this

syst

em,

4 st

eps

are

need

ed:

1.Is

ther

e ph

ase

inve

rsio

n at

the

top

surfa

ce?

2.Is

ther

e ph

ase

inve

rsio

n at

the

botto

m s

urfa

ce3.

Wha

t are

the

cond

ition

s fo

r con

stru

ctiv

e/de

stru

ctiv

e in

terfe

renc

e?4.

wha

t sho

uld

the

thic

knes

s d

be fo

r 3) t

o ha

ppen

?

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

19

n=1 n

=1.5

n=1

thin

film

ana

lysis

1.to

p su

rface

?2.

botto

m s

urfa

ce?

3.co

nditi

ons?

4.d?

1.to

p su

rface

: n1<

n 2so

pha

se in

vers

ion

1/2

2.bo

ttom

sur

face

: n1>

n 2so

no

phas

e in

vers

ion

3.co

nditi

ons:

1.co

nstru

ctiv

e: ra

y 1

and

2 m

ust b

e in

pha

se2.

dest

ruct

ive:

ray

1 an

d 2

mus

t be

out o

f pha

se b

y 1/

24.

if ph

ase

inve

rsio

n w

ould

not

take

pla

ce a

t any

of t

he s

urfa

ces:

cons

truct

ive:

2d=m

(diff

eren

ce in

pat

h le

ngth

=int

eger

num

ber o

f wav

elen

gths

)du

e to

pha

se in

vers

ion

at to

p su

rface

: 2d=

(m+1

/2)

since

the

ray

trave

ls th

roug

h fil

m: 2

d=(m

+1/2

)fil

m=(

m+1

/2)

/nfil

mde

stru

ctiv

e: 2

d=m

film

=m/n

film

12

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

20

Not

e

The

inte

rfere

nce

is di

ffere

nt fo

r lig

ht o

f diff

eren

tw

avel

engt

hs

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

21

ques

tion

n a=1

n b=1

.5

n c=2

Phas

e in

vers

ion

will

occ

ur a

ta)

top

surfa

ceb)

botto

m s

urfa

cec)

top

and

botto

m s

urfa

ced)

neith

er s

urfa

ce

n 1

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

22

anot

her c

ase

The

air g

ap in

bet

wee

n th

e pl

ates

has

var

ying

thic

knes

s.Ra

y 1

is no

t inv

erte

d (n

1>n 2

)Ra

y 2

is in

verte

d (n

1<n 2

)w

here

the

two

glas

ses

touc

h: n

o pa

th le

ngth

diff

eren

ce:

dark

frin

ge.

if 2t

=(m

+1/2

)co

nstru

ctiv

e in

terfe

renc

eif

2t=m

dest

ruct

ive

inte

rfere

nce.

12

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

23

ques

tion

Giv

en h

=1x1

0-5

m30

brig

ht fr

inge

s ar

e se

en,

with

a d

ark

fring

e at

the

left

and

the

right

.W

hat i

s th

e w

avel

engt

h of

the

light

?

2t=m

dest

ruct

ive

inte

rfere

nce.

m g

oes

from

0 (l

eft)

to 3

0 (ri

ght).

=2t/

m=2

h/m

=2x1

x10-

5 /30

=6.6

7x10

-7m

=667

nm

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

24

new

ton’

s rin

gs

spac

ing

not e

qual

dem

o

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

26

quiz

ques

tion

(ext

ra c

redi

t)

why

is it

not

pos

sible

to p

rodu

ce a

n in

terfe

renc

e pa

ttern

in a

dou

ble-

slit e

xper

imen

t if t

he s

epar

atio

n of

the

slits

is le

ss th

an th

e w

avel

engt

h of

the

light

use

d?a)

the

very

nar

row

slit

s re

quire

d w

ould

gen

erat

e di

ffere

ntw

avel

engt

h, th

ereb

y w

ashi

ng o

ut th

e in

terfe

renc

e pa

ttern

b)th

e tw

o sli

ts w

ould

not

em

it co

here

nt li

ght

c)th

e fri

nges

wou

ld b

e to

o cl

ose

toge

ther

d)in

no

dire

ctio

n co

uld

a pa

th d

iffer

ence

as l

arge

as

one

wav

elen

gth

be o

btai

ned

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

27

diffr

actio

n

In Y

oung

’s e

xper

imen

t, tw

o sli

ts w

ere

used

to p

rodu

cean

inte

rfere

nce

patte

rn. H

owev

er, i

nter

fere

nce

effe

cts

can

alre

ady

occu

r with

a s

ingl

e sli

t.

This

is du

e to

diff

ract

ion:

the

capa

bilit

y of

ligh

t to

be“d

efle

cted

” by

edg

es/s

mal

lop

enin

gs.

In fa

ct, e

very

poi

nt in

the

slit o

peni

ngac

ts a

s th

e so

urce

of a

new

wav

e fro

nt

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

28

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

29

inte

rfere

nce

patte

rn fr

om a

sin

gle

slit

pick

two

poin

ts, 1

and

2, o

ne in

the

top

top

half

of th

e sli

t, on

e in

the

botto

m h

alf o

f the

slit

.Lig

ht fr

om th

ese

two

poin

ts in

terfe

res

dest

ruct

ivel

y if:

x=(a

/2)s

in=

/2

so

sin=

/a

we

coul

d al

so h

ave

divi

ded

up th

e sli

tin

to 4

pie

ces:

x=(a

/4)s

in=

/2 s

o s

in=2

/a

6 pi

eces

:x=

(a/6

)sin

=/2

so

sin

=3/a

Min

ima

occu

r if s

in=m

/a m

=1,2

,3…

In b

etw

een

the

min

ima,

are

max

ima:

sin

=(m

+1/2

)/a

m=1

,2,3

…A

ND

sin=0

or

=0

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

30

slit w

idth

if>a

sin

=/a

> 1

N

ot p

ossib

le, s

o no

patte

rns

if

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

31

the

diffr

actio

n pa

ttern

The

inte

nsity

is n

ot u

nifo

rm:

I=I 0s

in2 (

)/2

=a(

sin)/

aa

aa

aa

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

32

ques

tion

light

with

a w

avel

engt

h of

500

nm

is u

sed

to il

lum

inat

ea

slit o

f 5m

. At w

hich

ang

le is

the

5th

min

imum

in th

e di

ffrac

tion

patte

rn s

een?

sin=m

/a=s

in-1

(5x5

00x1

0-9 /

(5x1

0-6 )

)=30

0

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

33

diffr

actio

n fro

m a

sin

gle

hair

inst

ead

of a

n sli

t, w

e ca

n al

so u

se a

n in

vers

eim

age,

for e

xam

ple

a ha

ir!de

mo

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

34

doub

le s

lit in

terfe

renc

e re

visit

ed

The

tota

l res

pons

e fro

m a

dou

ble

slit s

yste

m is

a

com

bina

tion

of tw

o sin

gle-

sour

ce sl

its, c

omb

ined

with

a di

ffra

ctio

n pa

ttern

from

ea

ch o

f the

slit

due

to d

iffra

ctio

n

due

to 2

-slit

in

terfe

renc

em

axim

ads

in=m

, m=0

,1,2

,3…

min

ima

dsin

=(m

+1/2

), m

=0,1

,2,3

…d:

dist

ance

bet

wee

n tw

o sli

ts

min

ima

asin

=m, m

=1,2

,3…

max

ima

asin

=(m

+1/2

), m

=1,2

,3…

and

=0a:

wid

th o

f ind

ivid

ual s

lit

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

35

doub

le-s

lit e

xper

imen

ta

if>d

, eac

h sli

t act

s as

a s

ingl

eso

urce

of l

ight

and

we

get

a m

ore

or le

ss p

refe

ct d

oubl

e-sli

tin

terfe

renc

e sp

ectru

m

if

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

36

7th

7th

A p

erso

n ha

s a

doub

le s

lit p

late

. He

mea

sure

s th

e di

stan

ce b

etw

een

the

two

slits

to b

e d=

1 m

m. N

ext h

e w

ants

to d

eter

min

e th

e w

idth

of e

ach

slit

by in

vest

igat

ing

the

inte

rfere

nce

patte

rn. H

e fin

ds th

at th

e 7t

hor

der

inte

rfere

nce

max

imum

line

s up

with

the

first

diff

ract

ion

min

imum

and

thus

van

ishes

. Wha

t is

the

wid

th o

f the

slit

s?

7th

orde

r int

erfe

renc

e m

axim

um: d

sin=7

so s

in=7

/d1s

tdi

ffrac

tion

min

imum

: asin

=1so

sin

=/a

sinm

ust b

e eq

ual f

or b

oth,

so

/a=7

/dan

d a=

d/7=

1/7

mm

ques

tion

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

37

diffr

actio

n gr

atin

g

d

cons

ider

a g

ratin

g w

ithm

any

slits

, eac

h se

para

ted

bya

dist

ance

d. A

ssum

e th

at fo

rea

ch s

lit

>d. W

e sa

w th

at fo

r 2 s

lits

max

ima

appe

ar if

:ds

in=m

, m=0

,1,2

,3…

This

cond

ition

is n

ot c

hang

ed fo

r in

the

case

of n

slit

s.

diffr

actio

n gr

atin

gs c

an b

e m

ade

by s

crat

chin

g lin

es o

n gl

as a

ndar

e of

ten

used

to a

naly

ze li

ght

inst

ead

of g

ivin

g d,

one

usu

ally

give

s th

e nu

mbe

r of s

lits

per

unit

dist

ance

: e.g

. 300

line

s/m

md=

1/(3

00 li

nes/

mm

)=0.

0033

mm

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

38

sepa

ratin

g co

lors

dsin

=m, m

=0,1

,2,3

…fo

r max

ima

(sam

e as

for d

oubl

e sli

t)so

=sin

-1(m

/d)

depe

nds

on

, the

wav

elen

gth.

cd’s

can

act

as

a di

ffrac

tion

grat

ing

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

39

ques

tion

If th

e in

terfe

renc

e co

nditi

ons

are

the

sam

e w

hen

usin

g a

doub

le s

lit o

r a d

iffra

ctio

n gr

atin

g w

ith th

ousa

nds

of s

lits,

w

hat i

s th

e ad

vant

age

of u

sing

the

grat

ing

to a

naly

ze

light

?a)

the

mor

e sli

ts, t

he la

rger

the

sepa

ratio

n be

twee

n m

axim

a.b)

the

mor

e sli

ts, t

he n

arro

wer

eac

h of

the

brig

ht s

pots

and

th

us e

asie

r to

see

c) th

e m

ore

slits

, the

mor

e lig

ht re

ache

s ea

ch m

axim

um

and

the

max

ima

are

brig

hter

d) th

ere

is no

adv

anta

ge

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

40

ques

tion

An

diffr

actio

n gr

atin

g ha

s 50

00 li

nes

per c

m. T

he a

ngle

betw

een

the

cent

ral m

axim

um a

nd th

e fo

urth

ord

erm

axim

um is

47.

20. W

hat i

s th

e w

avel

engt

h of

the

light

?

dsin

=m, m

=0,1

,2,3

…d=

1/50

00=2

x10-

4cm

=2x1

0-6

mm

=4, s

in(4

7.2)

=0.7

34so

=ds

in/m

=2x1

0-6 x

0.73

4/4=

3.67

x10-

7m

=367

nm

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

42

pola

rizat

ion

We

saw

that

ligh

t is

real

ly a

n el

ectro

mag

netic

wav

e w

ith

elec

tric

and

mag

netic

fiel

d ve

ctor

s os

cilla

ting

perp

endi

cula

r to

each

oth

er. I

n ge

nera

l, lig

ht is

un

pola

rized

, whi

ch m

eans

that

the

E-fie

ld v

ecto

r (an

d th

us

the

B-fie

ld v

ecto

r as

long

as

it is

perp

endi

cula

r to

the

E-fie

ld) c

ould

poi

nt in

any

dire

ctio

n prop

agat

ion

into

scr

een

E-ve

ctor

s co

uld

poin

tan

ywhe

re: u

npol

arize

d

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

43

pola

rized

ligh

t

light

can

be

linea

rly p

olar

ized,

whi

ch m

eans

that

the

E-fie

ld o

nly

osci

llate

d in

one

dire

ctio

n (a

nd th

e B-

field

pe

rpen

dicu

lar t

o th

at)

The

inte

nsity

of l

ight

is p

ropo

rtion

al to

the

squa

re o

f am

plitu

de o

f the

E-fi

eld.

I~E m

ax2

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

44

How

to p

olar

ize?

abso

rptio

nre

flect

ion

scat

terin

g

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

45

pola

rizat

ion

by a

bsor

ptio

n

certa

in m

ater

ial (

such

as

pola

roid

used

for s

ungl

asse

s)

only

tran

smit

light

alo

ng a

cer

tain

‘tra

nsm

issio

n’ a

xis.

be

caus

e on

ly a

frac

tion

of th

e lig

ht is

tran

smitt

ed a

fter

pass

ing

thro

ugh

a po

lariz

er th

e in

tens

ity is

redu

ced.

If

unpo

lariz

ed li

ght p

asse

s th

roug

h a

pola

rizer

, the

inte

nsity

is

redu

ced

by a

fact

or o

f 2

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

46

pola

rizer

s an

d in

tens

itypo

lariz

atio

nax

isdi

rect

ion

of E

-vec

tor

If E-

field

is p

aral

lel

to p

olar

izatio

n ax

is,al

l lig

ht p

asse

s

If E-

field

mak

es a

n an

gle

pol.

axis

only

the

com

pone

ntpa

ralle

l to

the

pol.

axis

pass

es: E

0cos

So I=

I 0cos

2

For u

npol

arize

d lig

ht, o

n av

erag

e, th

e E-

field

has

an a

ngle

of 4

50w

ithth

e po

lariz

er.

I=I 0c

os2

=I0c

os2 (

45)=

I 0/2

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

47

ques

tion

unpo

lariz

ed li

ght w

ith in

tens

ity I 0

pass

es th

roug

h a

linea

r pol

arize

r. It

then

pas

ses

thro

ugh

a se

cond

pol

arize

r (th

e se

cond

pol

arize

r is

usua

lly c

alle

d th

e an

alyz

er) w

hose

tran

smiss

ion

axis

mak

es a

nd a

ngle

of

300

with

the

trans

miss

ion

axis

of th

e fir

st p

olar

ized.

Wha

t is

the

inte

nsity

of t

he li

ght a

fter t

he s

econ

d po

lariz

er, i

n te

rms

of th

e in

tens

ity

of th

e in

itial

ligh

t?

Afte

r pas

sing

thro

ugh

the

first

pol

arize

r, I 1=

I 0/2.

Afte

r pas

sing

thro

ugh

the

seco

nd p

olar

izer,

I 2=I 1c

os2 3

0=0.

75I 1=

0.37

5I0

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

48

pola

rizat

ion

by re

flect

ion

If un

pola

rized

ligh

t is

refle

cted

, th

an th

e re

flect

ed li

ght i

s pa

rtial

ly

pola

rized

.if

the

angl

e be

twee

n th

e re

flect

ed ra

y an

d th

e re

fract

ed

ray

is ex

actly

900

the

refle

cted

lig

ht is

com

plet

ely

pola

rized

the

abov

e co

nditi

on is

met

if fo

r th

e an

gle

of in

cide

nce

the

equa

tion

tan

=n2/

n 1th

e an

gle

=tan

-1(n

2/n 1

) is

calle

d th

e Br

ewst

er a

ngle

the

pola

rizat

ion

of th

e re

flect

ed

light

is (m

ostly

) par

alle

l to

the

surfa

ce o

f ref

lect

ion

n 2

n 1

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

49

ques

tion

Beca

use

of re

flect

ion

from

sun

light

of t

he g

lass

win

dow

, th

e cu

rtain

beh

ind

the

glas

s is

hard

to s

ee. I

f I w

ould

wea

r po

laro

id s

ungl

asse

s th

at a

llow

… p

olar

ized

light

thro

ugh,

I w

ould

be

able

to s

ee th

e cu

rtain

muc

h be

tter.

a) h

orizo

ntal

lyb)

ver

tical

ly

horiz

onta

lve

rtica

ldi

rect

ion

of

pola

rizat

ion

of re

flect

ed

light

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

50

sung

lass

es

wea

ring

sung

lass

es w

ill h

elp

redu

cing

gla

re (r

efle

ctio

n)fro

m fl

at s

urfa

ces

(hig

hway

/wat

er)

with

out

with

sun

glas

ses

PHY2

32 -

Rem

co Z

eger

s

-in

terfe

renc

e, d

iffra

ctio

n &

pola

rizat

ion

51

pola

rizat

ion

by s

catte

ring

certa

in m

olec

ules

tend

to

pola

rize

light

whe

n st

ruck

by

it sin

ce th

e el

ectro

ns in

the

mol

ecul

es a

ct a

s lit

tle a

nten

nas

that

can

onl

y os

cilla

te in

a

certa

in d

irect

ion