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Polarization
1
a quick recap…
2
S =(E x B)/μo
Radiation intensity –Polar Plot
The angular distribution of the intensity of radiation
and its polarization state are shown
θ
I(θ)
Unpolarized light
Polaroid: Transmits along the pass axis and
absorbs along the perpendicular axis
Malus law
I  E  ( Eo cos  )  I o cos 
2
2
2
Unpolarized light
Io
I  I o cos  
2
2
Degree of polarisation
If the incident light is a mixture of unpolarised light of intensity Iu
and polarised light of intensity Ip, then the transmitted light is given by:
I max
Iu
2
I   I p cos 
2
Iu
Iu
  I p;
I min 
2
2
I max  I min
P
I max  I min
Polarisation by scattering
Rayleigh scattering
Blue sky
Red Sunset / Sunrise
Convention
- Polarisation
Plane of polarisation is same
as plane of incidence
- Polarisation
Plane of polarisation is perpendicular
to the plane of incidence
Polarisation by reflection
Brewster angle
unpolarised polarised
linearly polarised
partially polarised
Glass
Brewster angle
Brewster’s
law
= Brewster angle
Polarisation by reflection
Polarisation by double refraction
- Two refracted beams emerge instead of one
- Two images instead of one
Optic Axis: Uniaxial crystals exhibit cylindrical symmetry.
There is a unique direction in a uniaxial crystal called the optic axis.
Values of physical parameters along optic axis are different from the
values perpendicular to it.
Calcite
Quartz
Ordinary ray
Principal
Plane
Extraordinary ray
Optic axis
Calcite
Ordinary ray
σ - polarised
Calcite
Polariser/
Analyser
Extraordinary ray
π - polarised
Calcite
Polarisation by double refraction
Isotropic Medium : Velocity Spherical
Anisotropic Medium : Velocity ellipsoid
Uniaxial and Biaxial Crystals
Uniaxial : Calcite, Quartz
Biaxial: Mica
- Polarisation
Plane of polarisation is same as
plane of incidence (principal plane)
- Polarisation
Plane of polarisation is perpendicular
to the plane of incidence (principal plane)
Plane of incidence :
plane contains incident ray, reflected/refracted ray, surface normal
Plane of polarisation :
plane contains electric field vector and direction of propagation
Principal plane :
Plane contains optic axis and the direction of propagation
e-ray : Plane of polarisation is same
as principal plane
e-ray in general does not obey the laws of refraction
except in case of special cut of crystal (optic axis)
o-ray : Plane of polarisation is
perpendicular to the principal plane
o-ray always obeys the laws of refraction
Always
e-ray carries -polarisation
and
o-ray carries -polarisation
Linear polarisation by double refraction
Positive and Negative uniaxial crystals
Quartz -
no = 1.5443
Positive
ne = 1.5534
For sodium D lines
(ne - no)>0
ne > no
v e < vo
Calcite - Negative (ne - no)<0
ne < no
no = 1.6584
ne = 1.4864 v > v
e
o
Velocity or Refractive index is same along
the OPTIC AXIS for o-ray an e-ray.
Wave surface is the locus of all points reached by the ray at a given instant
Velocity ellipsoid
Positive crystal
ne > no
v e < vo
Quartz
Sphere
Spheroid
Positive crystal
Quartz
ne > no
Sphere ve < vo
Spheroid
Positive crystal
Quartz
ne > no
Sphere ve < vo
Spheroid
Calcite
Negative crystal
ne < no
v e > vo
Spheroid
Sphere
Calcite
Negative crystal
ne < no
ve > vo
Spheroid
Sphere
Calcite
Negative crystal
ne < no
ve > vo
Spheroid
Sphere
Biaxial
Huygens’
construction
Calcite
ne < no
ve > vo
Special cuts of uniaxial crystal
Optic axis normal to the surface of incidence
No double refraction
Optic axis parallel to the surface of incidence
No double refraction
Oblique Incidence
Optic axis parallel to the surface of incidence, normal to the plane of incidence
Dichroic crystals
Nicol
prism
Calcite
no = 1.6584
ne = 1.4864
Canada
balsam
n = 1.55
Rochon prism
Wollaston prism
Elliptical and circular polarisation
Plane polarised
Etc.
Circularly polarised
Production of elliptically polarised light
E
A
O
O=
E=
Retarders
Quarter wave, Half wave and Full wave
GLASS
Quartz
Half wave plate
Quartz
Babinet Compensator
is a
Variable retarder
C
. .. .. . .. . .
. . . . . . .. .. .. .. . . . .
.
Interference of polarised light
Fresnel-Arago laws
1. Two coherent rays polarised
at right angles do not interfere
2. Two parallel coherent polarised
rays will interfere in the same
way as will ordinary light
Problem 1
Problem 2
½ 1st FZ
.
P
P
1st FZ
Ans 1: I0/4
Ans 2: I0/2
Optically active medium
Rotation of the plane of vibration & Rotatary dispersion
Dextrorotatary or right handed medium
Levorotatary or left handed medium
Specific rotation
= 21.72 Deg/mm
for Sodium lines
Sugar, Glucose and Fructose
Specific rotation
Sugar
(Sucrose or Cane sugar)
Glucose-D
( Dextrose or Grape sugar)
Fructose
(Levulose or Fruit sugar)
66.47
52.7
- 92
o
o
o
Rotation in liquids
Specific rotation is defined as the observed rotation
of light of wavelength 589 nm (the d line of a
sodium lamp) passing through 10 cm of a 1 g ml-1
solution of a sample.
One can find out the density of substance in solution
Specific rotation, [ρ] = 10 θ / ld
θ = angle of rotation
l = Length of the liquid column in cm
d = density in gm/cm3
Fresnel’s explanation of rotation
Induced Optical Effects
Isotropic medium can be made optically anisotropic applying
1. Stress : Photoelastic Effect
2. Magnetic field : Faraday Effect
3. Electric field : Kerr effect
Faraday effect
d
B
=Verdet cosntant
0.00001-0.01 min
/Gauss-cm
Kerr effect
An isotropic medium becomes birefringent
by an application of electric field.
It behaves like an uniaxial crystal with
optic axis in the direction of applied field.
K = Kerr Constant