UNIT - III
POLARIZATION
Polarization is a property of waves that describes the orientation of their oscillations. In
transverse wave motion, the vibrations are always perpendicular to the direction of propagation.
Light waves are transverse waves. Therefore, in the propagation of light, the electric field
vibrations and the magnetic field vibrations are perpendicular to the direction of propagation. In
general the light having electric field vibrations in all directions perpendicular to the direction of
propagation. Such light is known as UNPOLARIZED LIGHT. This light is shown in figure.
If the electric field vibrations of a light are confined to a single plane, that light is called
PLANE POLARIZED LIGHT. This is shown in figure.
Polarization is also defined the light which has acquired the property of one-sidedness or
unsymmetrical about a direction of propagation is called POLARIZATION.
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POLARIZATION
In both these figures the direction of propagation is normal to the plane of the paper.
TYPES OF POLARISATION AND THEIR REPRESENTATION:
Linearly, Circular and Elliptical polarization:
Experimentally, it is found that the light exhibits the following three types of
polarization.
1. Plane polarized light
2. Circularly polarized light
3. Elliptically polarized light.
1. Plane Polarized light:
If the electric component of light passing through the medium vibrates only along
a single direction perpendicular to the direction of propagation, the wave is said to be
plane polarized or linearly polarized. This is shown in figure1.
The electric vector E can be resolved into two rectangular components Ex and Ey.
Therefore, the transverse electric vector may be regarded as superposition of two
mutually perpendicular electric fields. Thus
E=iEx+jEy
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POLARIZATION
Thus the vector E or linearly polarized is the superposition of two mutually perpendicular
waves having zero phase difference. This is shown in figure.
2. Circularly polarized light:
If two electric vectors Ex and Ey having same magnitude but vibrating in two
mutually perpendicular with phase difference π/2 radians super impose the magnitude of
the resultant vector E remains constant about the direction of propagation such that it
goes on sweeping a circular helix in space during the course of propagation. Such light
wave is called circularly polarized light. This is shown in figure2
If we imagine that we are looking into the light source and observe the rotation of
the light vector E, we observe that the tip of light vector E traces a circle on the plane
perpendicular to the ray direction. If rotation of the vector tip is clockwise, the light is
said to be right circular polarized. However, If it is rotates anticlockwise, the light is said
to be left circularly polarized.
3. Elleptically polarized light:
If the two electric vectors Ex and Ey having unequal amplitude vibrating in two
mutually perpendicular planes superimpose at phase which differ in π/2 radians, the
magnitude of the resultant vector E changes with time and vector E sweeps a flattened
helix in space. Such light wave is called elliptically polarized light. Shown in Fig3
Fig1
3
fig2
POLARIZATION
fig3
DOUBLE REFRACTION:
When a beam of ordinary unpolarized light is passed through a certain class of crystals
like calcite or Quartz, the refracted beam is split up into two refracted rays. This phenomenon is
known as “double refraction”. The crystals showing this phenomenon are known as double
“refracting crystals”. One of the refracted beams is found to obey the Snell’s law and is called
the ordinary ray (O-ray). The other refracted beam does not obey Snell’s law and is called the
extraordinary ray or E-ray. Both the rays are plane polarized and their vibrations are
perpendicular to each other (as shown in Fig.)
Upolarized light
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POLARIZATION
Ordinary and Extraordinary rays:
The ordinary ray travels in the crystal with same velocity in all direction. Therefore, the
refractive index for O-ray is constant.
The extraordinary rays travels in the crystal with a velocity that varies with direction. Thus
the refractive index for these rays varies with direction.
The quantities μ0 and μe are called the principal refractive indices for the crystal.
The ordinary ray has the same velocity in all directions and hence its wavefront is
spherical.
Extraordinary ray has different velocities in different directions and hence its wavefront
is ellipsoid.
In certain crystals, the ellipsoid lies outside the sphere i.e. the extraordinary wavefront
travels faster than ordinary wavefront except along optic axis. For such crystals μ0 > μe . These
crystals are known as negative crystals. Example Calcite and tourmaline.
In some other crystals the sphere lies outside ellipsoide i.e. the velocity of ordinary
wavefront is greater than extraordinary wavefront except along the optic axis. For such crysgtals
μ0 < μe . These crystals are known as positive crystals. Example Quartz.
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POLARIZATION
The difference between the refractive index of O-ray and E-ray is called birefringence
∆μ= μ0 −μe
The quantity ∆μ is maximum in the direction perpendicular to the optics.
Along the optics axis the quantity ∆μ=0
If ∆μ is positive, the crystal is called negative
If ∆μ is negative, the crystal is positive.
Both O-ray and E-ray are linearly polarized. They are polarized in mutually
perpendicular direction. The vibrations of O-ray is perpendicular to the principle section and Eray vibrations are parallel to the principle section.
Uniaxial Crystals:
Crystals in which there is only one direction of optic axis are known as un axial crystal
Example: calcite and quartz.
Biaxial Crystals:
Crystals in which there are two optic axes corresponding to both the blunt corners are
known as biaxial crystals.
Example mica gypsum topaz.
NICOL PRISM:
Principle:
When an unpolarized light is transmitted through a calcite crystal, it splits in ordinary and
extra-ordinary ray beams. These beams are completely plane polarized with vibrations
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POLARIZATION
perpendicular to each other. If by some means one beam is eliminated then the emergent beam
from calcite crystal will be plane polarized light. This is achieved by using a Nicol prism.
Working:
Nicol prism is constructed from calcite crystal whose length is three times as its width. The
crystal is cut in two pieces along a diagonal. Canada balsam cements the two cut surfaces
together. Canada balsam is a transparent substance for light. The refractive index of Canada
balsam lies between the refractive indices for the ordinary and extra-ordinary rays for calcite. For
sodium light the refractive indices are μo = 1.658, μcanada balsam = 1.55, μe = 1.486.
When a beam of unpolarized light enters into Nicol prism, it is doubly refracted into
ordinary plane polarized light and extra ordinary plane polarized light. From the values of
refractive indices, it is clear that Canada balsam acts as a rarer medium for an O-ray and denser
medium for an E-ray. Therefore, there exists a critical angle of refraction for the O-rays at calcite
Canada balsam surfaces but not for the E-rays. Therefore there exists a critical angle of refraction
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POLARIZATION
for the O-rays at calcite-canada balsam surface and but not for the E-rays. Under these
conditions, the ordinary ray is completely reflected at calcite-Canada balsam surfaces and is
absorbed by the tube as shown in Fig.
The value of critical angle φc =
= 690
The extra-ordinary ray is not totally reflected because it is traveling from a rarer to a
denser medium. Thus, only extra-ordinary ray is transmitted. Since extra-ordinary rays are plane
polarized, the light emerging from Nicol prism is plane polarized.
Limitations:
To obtain plane polarizeds light, the incident light should be confined within an angle of
140 on either side of the incident normal.
Nocol as polarizer and analyser:
Two Nicols lined up one behind the other are often used in optical microscopes for
studying optical properties of the crystal. The first Nicol, which is used to produce the plane
polarized light, is called the polarizer and the second Nicol, which is used to test the light, is
called the analyzer. In the parallel position light from the polarizer passes on through the
analyzer shown in figure (a) . Upon rotating the analyzer through 900 as shown in figure no light
is transmitted. In this case, E- ray in the second Nicol is totally reflected. In this situation the
both Nicols are crossed shown in fig(b).
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POLARIZATION
RETARDATION PLATES (OR QUARTER WAVE PLATE AND HALF WAVE
PLATE):
A retardation plate resolves a polarized light beam into two orthogonal components,
retards the phase of one component relative to the other and the recombines the two to form a
single beam with new polarization.
Two types of retardation plates are used in optical instruments.
1. Quarter wave Plate
2. Half wave Plate
1. QUARTER WAVE PLATE:
If the thickness of the crystal is such that it introduces a phase difference of /2 or a path
difference of /4, then the light emerging from this crystal is circularly polarized. Such a crystal
is called Quarter wave plate
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POLARIZATION
 Thickness of Quarter wave plate; t =

4 o   e 
2. HALF WAVE PLATE:
If the thickness of the crystal is such that it introduces a phase difference of  or path difference
/2, then the light emerging from this crystal is linearly polarized. A crystal plate of this type is
called half-wave plate.
Thickness of half wave plate t =

2 o   e 
Where o and e are refractive indices of the crystal for ordinary and extra ordinary
waves.
Note: When the phase difference is 0, , 2, 3, 4, ………………….. or path difference is 0,
   
, 2 , 3 , 4 ……the resultant light is a linearly polarized light.
2
2
2
2
If t is the thickness of the crystal and 0 , e refractive indices of the crystal for ordinary and
extraordinary rays.
t
n
2 e   o 
To produce linearly polarized the minimum thickness of the crystal is given by
t

2 e   o 
When the phase difference is /2, 3/2, 5/2, … or path difference is 0,
resultant light is a circularly polarized light.
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POLARIZATION



, 3 , 5 …the
4
4
4
If t is the thickness of the crystal and 0 , e refractive indices of the crystal for ordinary and
extraordinary rays.
t
2n  1
4 e   o 
To produce circularly polarized the minimum thickness of the crystal is given by
t
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POLARIZATION

4 e   o 