14. Production of polarized light
Malus’s Law : I = I
ocos
2θ
TE (transverse electric), s - polarization
Polarization
TM (transverse magnetic), p - polarization
Plane of incidence
Brewster’s angle
θ p
n
1n
2θr
=
°
= +
=
−
1 1 2
2 1
tan
90 ,
sin sin
n n n
n
p
r p
r p
θ
θ θ
θ θ
°
=
⇒
=
°
=
⇒
=
7 . 33
3 . 56
p p
1.0) air(n
to glass From
1.5) glass(n
to air From
θ θ θ p
Polarization by scattering
3 2 4 2
12 c r p e
: law scattering
h Rayleig
o o
πε
= ω
Index of refraction
{ }
−
∑ −
+
=
j i
j
o j j
f m
o Ne
ε
ω ω γ ωε
ω
ε
( 2 2)1 2 )
(
{ }
−
∑ −
+
≅
=
j
f m
Ne c
k c
j
o j i
j
o ω ω γ ω
ε
ε ω ε
ω
)
( 2 2
2 1 2
∑
+
− + −
≅
=
j j j
j f j
m r Ne
c k
n ( 2 2)2 2 2
2) ( 2
2 0 1 2
ω γ ω
ω
ω ω
ω ε
∑ − +
≅
=
j j j
j f j
c m Ne ki
2) 2 )2
2 (( 2
0 2 2 2
ω γ ω
ω
γ εω
α
ω εµ0)
= ( +
= kr iki since k k
Birefringence
Optical axis
d n
n
o
||
2 −
=
⊥λ ϕ π
∆
d
Birefringence : double refraction
Optical axis
Extraordinary ray Ordinary ray
OA
v||
v⊥
||
|| v v
n
n⊥ > ⇒ ⊥ <
Optical activity
t.
all for
then
, v v
or n n
k k
that Surpose
i E
E n c w k
e
E e
E E
i E
E n c w k
e
E e
E E
R L
R L
R L
R L
o oR
R L
wt z k i oL i
oR R
o oL
L L
wt z k i oL i
oL L
R R
L L
θ θ
θ θ
>
<
>
→
>
−
=
=
=
=
=
=
=
=
−
−
) , 1 )(
2 / ( ,
) / ( ,
) , 1 )(
2 / ( ,
) / ( ,
) (
) (
) (
) (
) (
,
R L
o
R 2 L
1 R
2 L 1 R
L
n z n
z k k
or
−
=
∴
−
=
−
= +
=
−
λ β π
θ θ
β β
θ β θ
EL
ER
θL
θR
β E
x y
Levorotatory: nL > nR
EL
ER
θL
θR
β E
x y
Dextrarotatory: nR > nL
R L
linear E E
E = +
