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Polarization
Interference and Diffraction
Wave nature of Light
WHY POLARIZATION ?
Longitudinal?
Transverse?
Light is an electromagnetic wave and
transverse in nature.
Natural light or ordinary light is unpolarized in
nature.
Vibrations take place symmetrically in all directions
in the plane perpendicular to the direction of
propagation of light.
Electric field only going up and down
 linearly or plane polarized
The process of transforming unpolarized light into
polarized light is known as
Electric field only going up and down – say it
is linearly polarized.
Representation of Plane polarized light
Plane polarized light with
Vibration perpendicular to
the Plane of paper (Spolarized)
Plane polarized light with
vibrations parallel to the plane
of paper (P-polarized)
Mathematical representation of
Plane polarized light
Suppose light is propagating in zdirection. Mathematically a plane
polarized light can be represented as:
E x  z, t   iE 0x cos  kz  t 
or
E y  z, t   jE 0y cos  kz  t 
Production of polarized light
1. By Reflection: Brewster’s Law
2. By Refraction: Malus Law
3. By selective absorption: Dichroic material
4. By double refraction:
-Nicol Prism
- Wave plates
Polarization by reflection: Brewster’s Law
• Unpolarized light is incident at
polarizing angle on the dielectric
medium the reflected light is
completely plane polarized.
  tan  p
Note : The polarizing angle is different for different
reflecting surfaces.
Polarization by reflection: Brewster’s Law
E-field radiation from electric dipole:
Polarization by reflection: Brewster’s Law
n 
2
 p  tan 1 
n 

 1
n1
n2
Show that  2   p 

2
sin p
n2
tan p 
 
cos  p n1
and Snell' s law
n1 sin p  n2 sin  2
Therefore
cos  p  sin 2  cos( 90   2 )
 p  2 

2
Polarization by reflection: Brewster’s Law
Polarization by reflection: Brewster’s Law
For air-water interface, n1 = 1 and n2 = 1.33 (say)
then Brewster’s angle is:
p = tan-1(1.33) ~ 530
Thus if the sunlight is incident on the sea at an angle
close to the polarizing angle, the reflected light is
almost polarized. Now if view through the rotation
Polaroid, the sea will appear more transparent
when the Polaroid blocks the reflected light.
Polarization by multiple reflection
Use of Polaroid
Use of Polaroid
Without polarizer
With polarizer
Use of Polaroid
Without polarizer
With polarizer
Polarization by double refraction
Discovered by Dr Dane Erasmus Bartholinus in 1669
When an UPL enters into an
anisotropic crystal, it splits into
two beams, each of them being
characterized by a certain state of
polarization. If by some method,
we could eliminate one of the
beams then we would obtained a
LPL.
Methods of eliminating one of the beam.
1. By selective absorption - Dichroism. e.g. tourmaline
2. Total Internal Reflection.
Polarization by Selective Absorption – Dichroism
The electric field component of an incident light that is perpendicular
to the optic axis (determined by its atomic configuration) is strongly
absorbed by the sample.
Thicker the sample, the more complete the absorption. Here the
crystal’s principal axis becomes polarizer’s transmission axis.
By total internal reflection
Polarization by Scattering
Law of Malus
Law
states
that
intensity of plane
polarized
light
transmitted through
the
analyzer
is
directly proportional
to the square of the
angle between the
transmission planes
of the polarizer and
analyzer.
I  I 0 cos 
2
Intensity of light transmitted through the analyzer
I = (E cos)2= E2 cos2  = I0 cos2 
When  = 00 i.e. pass axis of polarizer and analyzer
are parallel
I = I0
When  = 900 i.e. pass axis of
Transmission plane
polarizer is perpendicular to
Of polarizer
transmission plane of analyser
E
I=0
E sin
θ
E cos
Transmission plane of analyzer
Caution: Half
rule is applied
only when UPL
is allowed to
fall on polarizer.
• Unpolarized light is the superposition of many waves,
each with random polarization direction , relative to
fixed axis of polarizer.
• Each wave is attenuated by factor cos2.
• Average attenuation is <cos2> = 1/2
• Two consecutive polarizers.
• Two consecutive polarizers.
– The first polarizer reduces the intensity by half.
– The second polarizer reduces the intensity by
another factor of cos2.
– The second polarizer projects the electric field
onto a new axis, rotated by  from the axis of
the first polarizer
Wire Grid Polarizer
Input light contains
both polarizations
Spacing between the wires should be ≤ λ. Fabrication of
such a polarizer for 3 cm microwave is relatively easy. But
for optical region its quite difficult.
Effect of polarizer on transmitted light
1.
2.
3.
4.
5.
Un-polarized Light
Plane Polarized Light
Partially Polarized Light
Circularly Polarized Light
Elliptically Polarized Light
Quest: 22.10 (page-22.38) Optics 4th ed by Ajoy Ghatak
(a) Consider two crossed Polaroid's placed in the path of
an unpolarized beam of intensity I0. If we place a third
Polaroid in between the two then, in general, some
light will be transmitted through . Explain this
phenomenon.
(b) Assuming the pass axis of the third Polaroid to be 450
to the pass axis of either of the Polaroid's, calculate
the intensity of the transmitted beam. Assume that all
the Polaroid's are perfect.
Ans: I0/8
Quest: An unpolarized light passes through a
vertically placed polarizer having horizontal
polarization axis. Subsequently it passes through a
polarizer with its pass axis at 90o with respect to
vertical and two polarizers having their polarization
axes at an angle 30o and 60o with vertical
respectively.
What will be the intensity of the emergent light?
Ans : (3/32)I0