light as waves - Department of physics, uem jaipur · 2016. 9. 19. · PHY232 - Remco Zegers -...
Transcript of light as waves - Department of physics, uem jaipur · 2016. 9. 19. · PHY232 - Remco Zegers -...
-
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