Polarization of Light document discusses: 1. Huygen's construction is used to explain the wavefronts of ordinary and extraordinary rays when light interacts with birefringent crystals. The ordinary ray has a spherical wavefront while the extraordinary ray has an ellipsoidal wavefront. 2. When a beam of light is incident on a birefringent crystal, it is split into two rays - the ordinary and extraordinary rays. The ordinary ray travels with a constant velocity while the extraordinary ray's velocity depends on the direction. 3. Polarized light has vibrations confined to a single plane, while unpolarized light is a superposition of beams with random polarization. Polarizing materials only allow

1. POLARIZATION OF
LIGHT
DINESH V
ASSISTANT PROFESSOR
HOD OF PHYSICS
GOVT. FIRST GRADE COLLEGE, SAGAR

2. Huygen’s construction for O and E-wave fronts:
Assumptions: When a beam of light strikes the surfaces of doubly refracting crystal, each point on the surface
becomes the origin of two wave fronts which spreads out into the crystal. One for O-ray and another for E-ray.
For the O-ray, for which the velocity is constant in all direction, is a spherical wave front.
For the E-ray, for which the velocity is different in different directions, the wave front is ellipsoid..
The velocity of O-ray and E-ray are same along the optic axis and hence the crystal does not exhibit double
refraction, when the ray incident along optic axis. The spherical wave front corresponding to O-ray and ellipsoid
corresponding to E-ray will touch each other at any instant at points where these surfaces are cut by optic axis (in
fig). When the point source is placed inside the double refracting crystal, then the wave-fronts are spread out.

3. I. Optic axis in the plane of incidence and inclined to the crystal surface (refracting surface):
(i) Oblique incidence:

4. PQ-surface of the negative crystal
AB-plane wave front
A – source of two secondary wavelets
O-secondary spherical wave front for the ordinary ray
E-secondary ellipsoidal wave front for the extraordinary ray
CM-tangent to the O-ray at M
CN- tangent to the E-ray at N
Let “t” the time during which the incident wave front reaches
from B to C, so that t = BC/V
Where v = velocity of light in air
During the time t, the O-ray travelling a distance AM with a
velocity vo inside the crystal.
i.e., t =
𝐴𝑀
𝑉𝑜
∴
𝐵𝐶
𝑉
=
𝐴𝑀
𝑉𝑜
AM =
𝐵𝐶
𝑉
vo =
𝐵𝐶
𝑛𝑜
∵ n0 =
𝑉
𝑉𝑜
Where no = refractive index of ordinary ray

5. If ve is the velocity of E-ray along AN, then time “t” is
t =
𝐴𝑁
𝑉𝑒
𝐵𝐶
𝑉
=
𝐴𝑁
𝑉𝑒
∴ AN =
𝐵𝐶
𝑉
ve =
𝐵𝐶
𝑛𝑒
∵ ne =
𝑉
𝑉𝑒
Where ne = refractive index of extraordinary ray
AM is the radius of the ordinary spherical wave front.
The extraordinary ellipsoidal wave front has the semi-minor
axis along the optic axis AD
semimajor axis AG at right angles to the optic axis.
Therefore, the sphere drawn with A as center and AD =
𝐵𝐶
𝑛𝑜
as
the radius represent the ordinary wave surface.
The ellipsoidal drawn with AD =
𝐵𝐶
𝑛𝑜
as the semi-minor axis
and AG =
𝐵𝐶
𝑛𝐸
as the semimajor axis represent an extraordinary
wave surface, where nE is the principal refractive index for the
extraordinary ray and nE ˂ ne ˂ no.
Thus the ordinary and extraordinary rays travel in
different directions with different velocities.
The O-ray AO is perpendicular to the tangent CM
to the sphere whereas the E-ray AE is not
perpendicular to the tangent CN to the ellipsoidal.

6. (ii) Normal incidence:
*AB-plane wave front incident normally on PQ
The incident wave front AB is parallel both before
and after refraction.
MN is the refracted wave front tangential to the spherical wave front of ordinary ray and RS is the refracted
wave front tangential to the ellipsoidal wave front of extraordinary ray.
Both ordinary and extraordinary wave fronts MN and RS are parallel to the refracting surface.
Since AO is perpendicular to MN and AC is not perpendicular to RS the ordinary and
extraordinary rays travel along different directions.

7. II. Optic axis in the plane of incidence and Parallel to the refracting surface:
(i) Oblique Incidence:
AB-obliquely incident wave front on PQ
The optic axis in the plane of incidence is parallel to the PQ.
The refracted spherical and ellipsoidal wave surfaces touch each
other along the line PQ (optic axis) as shown in fig.
Therefore ordinary and extraordinary rays travel with different velocities in
different directions.
The semi-minor axis of the ellipsoidal is equal to AM =
𝐵𝐶
𝑛𝑜
.
The semimajor axis of the ellipsoidal is equal to AN =
𝐵𝐶
𝑛𝐸
Where nE is the principal refractive index for extraordinary ray and nE < ne < no.
The ordinary ray obey the ordinary laws of refraction whereas extraordinary does not obeys, since its velocity
varies with direction. Both the rays are plane polarized.

8. (ii) Normal Incidence:
Let AB is the wave front which is incident normally on the refracting
surface PQ of negative crystal.
The optic axis is in the plane of incidence and parallel to the crystal surface PQ. MN is the refracted wave front
tangential to the spherical wave front of O-ray and RS is the refracted wave front tangential to the ellipsoidal wave
front of E-ray.
Both the wave fronts MN and RS are parallel the refracting surface. AO & AE are ordinary and extraordinary rays
both travelling along the same direction with different velocities.
Therefore a definite path difference is introduced between the O-ray and E-rays. This principle is used in the
construction of quarter-wave and half-wave plates.

9. Electromagnetic Wave

10. EM wave is …
• Light is an electromagnetic wave.
• It consists of vibrations of electric field and magnetic field.
• The electric field and magnetic field are perpendicular to each other and in
phase.
• EM wave is a transverse wave.
• The speed of EM wave is 3 x 108 ms-1.

11. Electric Field Vector

12. Polarized Light
Polarized Light
Vibrations lie on one single
plane only.
Unpolarized Light
Superposition of many beams,
in the same direction of
propagation, but each with
random polarization.

13. Representation . . .
Unpolarized Polarized
EE

14. Representation . . .
Unpolarized Polarized

15. Polarization of Light

16. Selective Absorption
Light
Unpolarized
Horizontal Component
being Absorbed
Vertical
Component
being
Transmitted

17. Selective Absorption - Explanation

18. Polarizing Material
A Polarizing material will
only allow the passage of
that component of the
electric field parallel to
the polarization direction
of the material
I = I0 cos2q

19. Polarizer & Unpolarized Light
• Each wave is attenuated by factor cos2q.
• Average attenuation is < cos2q > = 1/2

20. Crossed Polarizers
• The first polarizer reduces the intensity by half.
• The second polarizer reduces the intensity by another factor of cos2q.
• The second polarizer projects the electric field onto a new axis, rotated by q
from the axis of the first polarizer

21. Crossed Perpendicularly

22. Crossed at different angles . . .

23. N. Manset / CFHTPolarization of Light: Basics to Instruments 23
Circular polarization (IV)
Part I: Polarization states, circular polarization... see it now?

24. N. Manset / CFHTPolarization of Light: Basics to Instruments 24
Elliptical polarization
Part I: Polarization states, elliptical polarization
• Linear + circular polarization = elliptical polarization

25. Polarization of Light: Basics to Instruments
Unpolarized light
(natural light)
Part I: Polarization states, unpolarized light

26. Polarization of Light: Basics to Instruments
Retarders
• In retarders, one polarization gets ‘retarded’, or delayed, with respect to the other
one. There is a final phase difference between the 2 components of the
polarization. Therefore, the polarization is changed.
• Most retarders are based on birefringent materials (quartz, mica, polymers) that
have different indices of refraction depending on the polarization of the incoming
light.
Part III: Optical components, retarders

27. Polarization of Light: Basics to Instruments 27
Half-Wave plate (I)
• Retardation of ½ wave
or 180º for one of the
polarizations.
• Used to flip the linear
polarization or change
the handedness of
circular polarization.
Part III: Optical components, retarders

28. Polarization of Light: Basics to Instruments
Half-Wave plate (II)
Part III: Optical components, retarders

29. 29
Quarter-Wave plate (I)
• Retardation of ¼ wave or 90º for one of the
polarizations
• Used to convert linear polarization to elliptical.
Part III: Optical components, retarders

30. N. Manset / CFHTPolarization of Light: Basics to Instruments 30
• Special case: incoming light polarized at 45º with respect to the retarder’s axis
• Conversion from linear to circular polarization (vice versa)
Quarter-Wave plate (II)
Part III: Optical components, retarders