Polarization

The phenomenon in which the

vibrations of the particles of the
medium produced by light waves are
restricted to one particular direction or
plane is called polarization of light
waves.

S1 S2

S1 S2

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➢The transverse wave is parallel to the slit S1. If the slit S2 is
also parallel to slit S1, then light will be pass without any
change.
➢If the slit S2 is perpendicular to slit S1, then S2 does not
allow the wave to pass through it.
➢If longitudinal waves are up by moving the rope forward
and backward along the sting, the waves will pas through S1
and S2 irrespective of their position.

From this experiment we can say that light is a transverse

2
wave
 Plane of polarization & Plane of vibration
Plane of
vibration

Plane of
polarization

The plane containing the

direction of vibration and
direction of propagation of light
is called the plane of vibration.

The plane passing through the direction of

propagation and containing no vibration is
called plane plane of polarization.
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(a). Vibrations are parallel and perpendicular to the plane
of the paper.
(b). The vibrations are only parallel to the plane of the
paper
(c). The vibrations are only perpendicular to the plane of
the paper.

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Methods of producing Plane polarized light

1. Polarization by reflection,
2. Polarization by refraction,
3. Polarization by double refraction,
4. Polarization by scattering and
5. Polarization by selective absorption.

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 Polarization by Reflection (discovered by Malus in 1808)

AB is the incident light

BC is the reflected light

If the Tourmaline crystal is rotated

slowly then at a particular angle of
incidence light will be completely
extinguished 6
Malus Law
According to malus, when completely plane polarized light is
incident on the analyzer, the intensity I of the light transmitted
by the analyzer is directly proportional to the square of the
cosine of angle between the transmission axes of the analyzer
and the polarizer.
i.e,
I cos 2 

Intensity is maximum when the two planes are parallel

Intensity is minimum when the two planes are perpendicular.

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When the incident polarized light of amplitude Ao strikes
the analyzer at an angle θ, it is resolved into two
components Aocosθ and Aosinθ as shown in Fig. The
component Aosinθ will be absorbed by the analyzer.
Since, only Aocosθ passes through the analyzer the
amplitude of the transmitted light is therefore,

A= Aocosθ (1)

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So, the amplitude of polarization of the transmitted wave is proportional
to the cosine of the relative angle (θ). Since intensity (I) is the square of
the amplitude (A), it can be expressed as

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 Brewster’s Law (discovered by Brewster in 1811)
The angle of incidence that produces 90° angle between the
refracted and reflected light wave is called Brewster angle.

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When the light falls on the medium at Brewster angle, the
reflected wave has no electric field vectors that are parallel
to the refracted ray. The only direction possible for the light
wave is perpendicular to the plane of the image. So, the
reflected wave is completely polarized. Whereas, the
refracted wave is partially polarized.

The tangent of the angle of polarization is numerically

equal to the refractive index of the medium.

 = tan i
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 From snell’s law
sin i
= ................(1)
sin r
From Brewster’s law
sin i
 = tan i = ............(2)
cos i
Comparing (1) and (2)
 
cos i = sin r = cos − r 
2 

i = −r
2

or , i + r =
2
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The reflected light and refracted light should be
perpendicular to each other.
Hence, we can write, i+r+90=180
⇒ i+r=90

So the angle CBD is equal to 90˚.

Therefore reflected and refracted rays are at right
angle to each other.

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Application of Brewster’s law:
(1) It can be used to determine the refractive indices of
opaque materials.
(2) It helps us in calculating the polarizing angle necessary
for total polarization of reflected light for any material if
its refractive index is known. However, the law is not
applicable for metallic surfaces.
(3) Two windows known as Brewster windows are used in
gas lasers.
(4) Another application utilizes the Brewster angle for
transmitting a light beam into or out of an optical fiber
without reflection losses.

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 Polarization by double refraction
( discovered by Erasmus Bartholinus in 1669)

When a ray of light is refracted by a crystal of calcite, it

gives two refracted rays. This phenomenon is called
double refraction.

BO=Plane polarized plane in

one plane
BE=plane polarized in a
perpendicular plane.

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There are two refractive indices

sin i sin i
1 = , 2 =
sin r1 sin r2 ,

If angle of incidence varies snell’s law holds for one of the rays,
BO which is known ordinary ray. In which refractive index is
constant (say μ0)
but other ray does not generally hold. In this case refractive
index varies with direction.(say μe)

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In double refracting crystals there is one particular
direction
in which both the ordinary and extraordinary rays travel
with equal velocities
Refractive index of the crystal for both E-ray and O-ray is
same.
In this direction the crystal will not exhibit double
refraction.
This direction is known as optic axis.

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 Crystals in which the extraordinary ray
travels faster than the ordinary is called
negative crystal (Calcite,no>ne), and reverse
is the positive crystal (Quartz, no<ne).

In a doubly refracting crystal , a plane containing the optic

axis and perpendicular to its opposite faces is called its
principle section.
The vibrations are in the ordinary rays are perpendicular to
the principle section, therefore O-ray is polarized in the
principle section
In the extraordinary rays vibrations are in the principle
section of the crystals , therefore E-ray is polarized
perpendicular to the principle section
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 Nicol Prism (William Nicol in 1828)

Construction:
▪Negative uniaxial crystal, calcite(n0=1.6584 and ne=1.4864 for λ
=589.3nm)
▪Two triangular sections are optically coupled at the hypotenuse by a
thin coating of optically clear cement, canada balsam(ncement≈1.55)
with the optic axis direction.
Calcite is widely used because of its clarity, stability, high spectral
transmission range and high birefringence.
•Its length is three times as that of its breadh
•AB'CDEFGH' is a calcite crystal, B' and H' are blunt
corners.
•The plane B'DH'F is perpendicular to AB'CD and EFGH'
and known as principle section of the crystal.
•B'DH'F is a parallelogram and its angle are71⁰ and 108 ⁰
•The angles B'DH' and B'FH' are 71 ⁰
•AB'CD and EFGH' are grounded in such a way that the
angles B'DH' and B'FH' are reduced from 71 ⁰ to 68 ⁰
•ABCD and EFGH be the new upper and lower faces of the
crystal
•The new principle section is BDHF
•The crystal is cut into two along the plane JHKB
•The plane JH'KB' is perpendicular to the principle section
B'DH'F
The two cut surfaces are highly polished into optical flatness and then
cemented together with Canada balsam, a transparent glue so that the
crystal is just as transparent as it was previously to its having been
sliced.
Working Principle

Unpolarized light

Ordinary ray Extra-Ordinary ray

Ordinary or o-ray undergoes total The extraordinary ray or e-ray

internal reflection at the calcite- does not undergoes total internal
glue interface because its angle of reflected at the interface because it
incidence at the glue layer strikes the interface at a sub-
(refractive index μ = 1.55) exceeds critical angle. The e-ray merely
the critical angle for the interface. undergoes a slight refraction, or
It passes out the top side of the bending, as it passes through the
upper half of the prism with some interface into the lower half of the
refraction as shown. prism. It finally leaves the prism as
a ray of plane polarized light.
Nicol prism as a polarizer and as an analyzer

Nicol prism as Polarizer and analyzer (a) parallel position (b) crossed position

The first nicol prism is known Polarizer (P), since it polarized the light
 The two prisms are placed with their principle
sections parallel to each other. Then the e-ray transmitted
by polarizer is freely transmitted by the other.

No light comes out when they are in crossed

position. Because when the extraordinary rays enters into
the second nicol prism , it acts as an ordinary ray and is
totally internally reflected.

Dichroism:Crystals and minerals which are doubly refracting

and have the property of absorbing the ordinary and extraordinary
rays unequally are said to be dichroic and the phenomenon is
called dichroism. In this way plane polarized light can be
produced.
Polaroid
Polaroid is an artificial crystalline material
which can be made in thin sheets and has the
property of producing plane polarized light by
the method of selective absorption.

Large sized polarizing films mounted between two

thin glass plates.
The film comprises of a thin sheet of nitrocellulose
containing ultramicroscopic crystal of herapathite (an
organic compound of iodine and quinine sulphate)
arranged such that optic axis of all of them are Two polaroids in parallel
parallel to make them function together as a single and crossed position
crystal of large dimension. This crystals can absorb
one of the doubly refracted beams completely with a
very small thickness of the order of 0.005inch

The emergent beam is plane polarized when the two pieces of polaroids are
parallel (Fig.a) and perfectly extinction when they are crossed (Fig.b)
 Application of polaroid

1. For producing and analyzing polarized light.

2. They are relatively less costly compared to nicols, hence they
are used in modern polarizing instruments.
3. To control the intensity of light in trains and airplanes
4. To produce three dimensional moving pictures.
5. To improve the color contrast in old oil painting.
6. They are used in sunglasses, windscreens, etc.
7. They are also used in studying optical properties of metals and
in analyzing crystals.
8. To eliminate the head light glare in motor cars.
wave plate or Retarding plate: A wave plate is an optical
device that alters the polarization state of light by introducing a
phase shift between its two perpendicular polarization
components.
A retarding plate resolves a polarized light beam into two
orthogonal components, retards the phase of one component to
other and then recombine the two to form a single beam with
new polarization characteristics.

It can be classified into three types-

1) Full wave plate
2) Half wave plate
3) Quarter wave plate
Quarter wave plate: (This type plate is widely used for the production and the
detection of elliptically and circularly polarized light.)

A plate of doubly refracting uniaxial crystal of calcite or quartz of

suitable thickness, whose refracting faces are cut parallel to the
direction of the optic axis.

The thickness of the plate is such as to produce a phase shift π/2 or

path difference λ/4 between the ordinary and extraordinary ray.

The velocity of the E-ray is greater than the velocity of the O-ray.
So a phase difference is introduced between them.

Let,
t=thickness of the plate
μo=refractive index for ordinary ray
μe =refractive index for extraordinary ray

Path difference
 o t −  e t = (  o −  e )t
 For quarter wave plate
(  o −  e )t =  / 4

t=
4(  o −  e ) For positive crystal

If the plane polarized inclined at an angle of 450 with the optic

axis of the plate then the emerged light is circularly polarized.
If the plane polarized light do not make an angle of 450 ,00 ,or 900
with the optic axis of the plate then the emerged light is elliptically
polarized.

(b) Circularly polarized light (c) Elliptically polarized light

Half wave plate(This type plate is widely used in the Laurentz
half-shade polarimeter for the measurement of optical rotation.)

 o t −  e t = ( o −  e )t

(  o −  e )t =  / 2

t= For negative crystal
2(  o −  e )

If the plane polarized makes an angle θ with the optic axis of the plate
then the emerged light is also plane polarized at an angle 2θ with the
optic axis.
Optical activity
It is the ability of a chemical substance to rotate
the plane of vibration of plane polarized light to the
left or right.
The substance which can show this phenomenon is called
optical active substance.
Dextrorotary positive or right side or clockwise rotation

Levorotary negative or left side or anticlockwise rotation

Calcite is not a optically active substance but Quartz is .

Sugar crystal, sugar solution, turpentine, sodium
chlorate and cinnabar are optical active substance.

Optical activity depends on several factors:

concentration of the sample, temperature, length of the
sample tube or cell, and wavelength of the light passing
through the sample.
Specific rotation: The change in orientation of the plane of linearly
polarized light as this light passes through a sample with a path
length of 1 decimeter and a sample concentration of 1 gram per 1
millilitre.

It depends on:
thickness of the medium, concentration of the solution
or density of the active substance in the solvent,
wavelength of light and temperature.

10
=
'
S
lc

S’λ represent the specific rotation at temperature, t0C

λ is the wavelength
θ is the angle of rotation
l is the length of the solution
C is the concentration of the substance in gm/cc
Polarimeter:
A polarimeter is a scientific instrument used to measure
the angle of rotation caused by passing polarized light through an
optically active substance.

Types
-Laurent’s half-shade polarimeter
-Biquartz polarimeter
-Lippich polarimeter
-Quartz-wedge polarimeter
Laurent’s half-shade polarimeter
Polarizer is fixed but the analyzer can freely rotate about a
common axis of the polarizer and analyzer. The rotation of the
analyzer can be observed on a graduated circular scale.

Half shade device is made in such a way that it gives the

path difference λ/2 between the E-ray and O-ray.
Basically it is a semicircular plate consists
-half part is made of glass and half part is made
of quartz, which can be rotated freely.
-Glass gives the single refraction but Quartz
gives the double refraction
 When the ray falls on the half shade device, four cases take place

1. If the principle plane A is parallel to PQ, the light from the glass portion will
pass unobstructed while light from the quartz will be partly obstructed, then
the glass part will appear brighter than quartz.
2. If the principle plane A is parallel to RS, the light from the quartz portion will
pass unobstructed while light from the glass will be partly obstructed, then the
quartz part will appear brighter than glass.
3. If the principle plane A is parallel to AC, both half will be bright.
4. When light falls perpendicular to the optic axis,ie. BD both half will be dark.