Prof. Vilas shamrao Patil

1. Department of Physics
B.SC.II
Sem-IV. Paper-VIII
DSC-D2- Waves and Optics-II
Topic- Polarisation of Light

2. 3.1 Introduction:-
We know that Huygens wave theory of light gave successful
explanation for interference and diffraction which proved, beyond
doubt, that light is in the form of waves. The exact form of light-
waves i.e. whether longitudinal or transverse can only be shown by
the observation of another important property of light viz.
polarisation.
The study of polarisation rather began with the study of double
refraction in certain naturally occurring crystals like calcite by
Huygens in 1690. He noticed that one of the refracted beam shows
symmetric character (ordinary) while other shows assymmetric
character (extra ordinary).
Fresnel explained the polarisation by considering that light
waves are transverse in nature. Maxwell's electromagnetic
wave theory also demands that they are transverse waves
with electric (𝐸) and magnetic ( 𝐵 ) vectors being mutually
perpendicular to the direction of propagation. in modern
days the plane containing electric vector 𝐸 and direction of
propagation was known as plane of vibration. However, now
it is a common practice to refer 'the plane containing electric
vector 𝐸and direction of propagation a plane- of
polarisation.

3. 3.2 Idea of Polarisation :-
If the electric vibrations of light wave are confined to
a single plane, then the light wave is said to be plane
polarised (or linearly polarised). symbols as shown in
Fig. 3.1 (a and b) in in which plane of vibration is a in
the plane of paper and b in a direction perpendicular
to the pane of paper.
In any natural source of light, there are
millions of atomic sources each of which
emit a short wave train of light for a time
period about 10-8 seconds i.e. millions of
such wave trains are emitted with
vibrations of electric vector oriented in all
possible directions i.e. the vibrations are
symmetrically distributed and such waves
are called unpolarised which may be
represented as shown in Fig. 3.1(c). As
each vibration can be decomposed into
two mutually perpendicular directions,
the unpolarised Fiat may also be
represented by the symbol as shown in
Fig. 3.1(d).

4. Unpolarised light from any source can be polarised by following methods
viz.
(i) by reflection
(ii) by refraction
(iii) by selective absorption
(iv) by double refraction.
3.3 : Polarisation by Double Refraction:-
The refraction through transparent substances like glass produces
a point image of a point object and refraction obeys Snell's laws
viz. (i) the incident ray, refracted ray and the normal to the surface
at the sin i point of incidence are in same plane (ii)
sin 𝑖
sin 𝑟
= 𝜇 , is a
constant called refractive index of the medium i.e. velocity of light
is same in all directions i.e. medium is isotropic. But there are
certain naturally occurring crystals like calcite and quartz which
produce two point images of a point object, showing that the
refracted ray splits into two rays viz.
(i) Ordinary ray : Ordinary ray is one which obeys Snell's laws,
i.e. velocity of 0-ray is isotropic i.e. same in all directions.
(ii) Extray-ordinary ray : Extray-ordinary ray (E-ray) does not
Obey Snell’s law Lc. the incident ray and refracted ray may
not be in the
same plane and velocity of E-ray is anisotropic Le. the
velocity of E- ray (and hence refractive index 𝜇𝑒) is different
in directions, Both ordinary and extra-ordinary rays are plane
polarised but in directions mutually perpendicular to each
other.

5. Double refraction by calcite crystal, when unpolarised-ray is
incident normally on principal section.
When an unpolarised light is incident normally on principal
section (i.e. plane containing optic axis and normal to any
of the cleavage face where optic axis is a direction along
which both 0-ray and E-ray have same velocity) as shown in
Fig. 3.2. Due to doubly refracting property of the calcite
crystal, the incident ray splits into 0-ray and E-ray. 0-ray
obeys Snell's laws and hence travels undeviated, whereas
E-ray which does not obey Snell's laws deviates i.e. refracts
and travels as shown in Fig. 3.2. The emergent 0-ray and E-
ray are parallel to each other. E-ray is plane polarised in the
principal section i.e. the vibrations of Electric field (E) are
parallel to the principal section whereas 0-ray are plane
polarised in a direction normal to the principal section.
If one of the ray (either 0-ray or E-ray) is removed from
the emergent beam, then we get polarised emergent
rays. This is done in Nicol prism, which produces
polarised light from the incident unpolarised light.

6. Huygen's Explanation of Double Refraction Through
Uniaxial Crystals:-
The naturally occurring crystals like calcite and quartz
exhibit double refraction i.e. the incident unpolarised light
splits into 0-ray and E-ray due to double refraction. 0-rays
have same velocity in all directions (i.e isotropic) and E-rays
have different velocities in different directions (i.e.
Anisotropic). But there is one direction in the crystal along
which both O-ray and E- ray have same velocity ( 𝑉
𝑜 = 𝑉
𝑒 )
and hence same refractive indices (𝜇𝑜 = 𝜇𝑒) and that
direction is called optic axis of the crystal, Since there is
only one such direction i.e. optic axis such crystals are
called uniaxial crystals.
Huygens gave an explanation for double refraction through
uniaxial crystals, using his theory of construction of
wavefronts.
(Fig. 3.3 Huygen's wavefronts for .E-ray and 0-ray in (a) Calcite
(negative crystal) (b) Quartz (positive crystal).
If P is a source point in the crystal, then it produces two
wavefronts, one for 0-ray and another for E-ray. Since 0-ray
has same velocity in all directions, the corresponding
wavefront is a sphere. But for E-ray, the velocity is different in
different directions and hence the corresponding wavefront
is an ellipsoid (as shown in Fig. 3.3).

7. Optic axis is a direction along which both 0-ray and E-ray
have same velocity and hence the two wave-fronts (or
wave surfaces) touch each other tangentially. Depending
upon the relative velocity of E-ray With respect to the
velocity of 0-ray, there are two types of uniaxial double
refracting crystals viz. (a) negative crystal and (b) positive
crystal.(a) Negative crystal - In case of calcite crystal (𝑉
𝑜≥
𝑉
𝑒 ) and hence the spherical wave surface corresponding
to 0-ray is inscribed in the ellipsoid corresponding to E-ray
as shown in Fig. 3.10). The two Waves surface touch each
other along optic axis. The velocity of E-ray is maximum
equal to 𝑉𝐸 in a direction normal to the optic axis. since
refractive index of material is the ratio of velocity (c) of
light in vacuum to the velocity (v) of light in the material
medium i.e. 𝜇 =
𝑐
𝑣
we have
𝝁𝟎 =
𝒄
𝒗𝟎
, 𝜇0=
𝑐
𝑣0
and =
𝑐
𝑣𝐸
But 𝑣𝐸 > 𝑣𝑒 > 𝑣𝑜 we get 𝜇𝐸< 𝜇𝑒< 𝜇0
Such crystals are called negative crystals.
(b) Positive crystals- In case of quartz crystal 𝑣𝑒 ≤ 𝑣0, and
therefore the ellipsoidal wave surface corresponding to E-ray
is inside the spherical wave surface corresponding to 0-ray as
shown in Fig, 3.3(b). The two wave surfaces touch each other
along the optic axis of the crystal and along the optic axis
𝑣𝑒 = 𝑣0 or( 𝜇𝑒> 𝜇0). The velocity of E-ray is minimum along
a direction normal to the optic axis. If VE is the minimum
velocity, then VE < Ve < Vo or 𝜇𝐸> 𝜇𝑒> 𝜇0
Since the 𝜇𝑒> 𝜇0 the crystal (quartz) is called positive
crystal.

8. 5 Characteristic Properties of Calcite
Crystal:-
Calcite is a naturally occurring, double refracting,
anisotropic crystal. Chemically it is CaCO3. The crystal,
when struck, it undergoes cleavage i.e. breaks into
smaller pieces each of which is a rhombohedra. Each
face of rhombohedron is a parallelogram with angles
78° and 102°.
There are two corners of the crystal (viz. B and H, opposite to
each other) which are made up of three edges meeting at B
and H making obtuse angles (102°) and hence they are called
blunt corners (Fig. 3.4(a)). A line bisecting the blunt corner
i.e. equally inclined with each edge is optic axis of the crystal.
In fact any line parallel to this is also optic axis. Thus, optic
axis is a direction along which the 0-ray and E-ray travel with
same velocity or it is axis of symmetry.
A plane containing optic axis and normal to a pair or
opposite faces is called principal section. Since there are
three pairs of opposite faces, there are three principal
sections. The principal sections cut the cleavage faces in a
parallelogram with angles 71° and 109° as shown in Fig.
3.3(b).

9. Nicol prism is an optical device commonly used as a
polarises as well as analyser i.e. to produce polarised light
and to analyse the state of polarisation of light respectively.
Nicol prism designed by William Nicol in 1820 is made up
of calcite crystal.
Construction and Working:- The construction or Nicol
prism is such that it removes one of the refracted rays (0-
ray) by total internal reflection so that the other refracted
ray (E -ray) is plane polarised emergent ray.
Fig. 3.5 Construction and working of Nicol prims.
To construct a Nicol prism, first of all a calcite crystal whose
length is three times the width is selected. The ends of
rhombohedron are ground until the angle of 710 in the
principal section is reduced to 680 Then the crystal is cut
along a plane (AC) perpendicular to both principal section
and the end faces. The two cut faces are ground and
polished optically flat and finally they are cemented together
using a transparent material called Canada balsam as shown
in Fig. 3.5. The refractive index of Canada balsam lies in
between those for 0-ray and E-ray in calcite,
For example, for sodium light (5890 A°). 𝜇0 = 1.658,
𝜇Canada balsam ( 𝜇𝐵) = 1.55, ( 𝜇𝐸)= 1.486.

10. Working of Nicol Prism- Canada balsam is optically denser than
calcite for E-ray ( 𝜇𝐵> 𝜇𝐸) and for 0-ray balsam is rarer (less dense)
than calcite ( 𝜇𝐵< 𝜇𝐸). The unpolarised light incident on the Nicol
prism undergoes double refraction i.e. splits into ordinary and
extra-ordinary rays. For ordinary-ray, calcite is denser medium than
balsam and hence for large angle of incidenses on the surface of
balsam, the 0-ray gets reflected totally internally. The critical angle
of incidence is about 69°. However, the E-ray is refracted into the
balsam and then into the calcite as shown in Fig. 3.5. Thus, the 0-
ray is removed from the emergent beam which is only E-ray. The 0-
rays suffering reflections at balsam layer are absorbed by
blackened surface of Nicol prism.
Since 0-ray and E-ray are both polarised in mutually perpendicular
planes, we see that the emergent E-ray is plane polarised with the
plane of polarisation parallel to the principal section of calcite
crystal. Thus, Nicol prism acts as a polariser as the emergent beam
is plane polarised.
• Nicol prism as an analyser : The Nicol prism can also be
used as an analyser i.e. to test the state of polarisation. First
a Nicol prism (P) is used to used lo obtain a polarised light.
This polarised light when incident on another Nicol prism
(A) with its principal section parallel to that of P, the E-ray
just passes through (A) and we receive full intensity in the
emergent beam (Fig. 3.6(a)).
• Now if the Nicol prism (A) is rotated about the incident
direction, intensity of emergent light goes on decreasing
and finally becomes then zero Le. no light emerges when
the principal section of (A) becomes normal to that of P. In
this case E--ray behaves as 0-ray for A. and hence is totally
reflected internally. This position of A with respect to P is
called crossed Position as shown in Fig. 3.6(b). Thus, Nicol
(A) is used to test the state of polarisation of light incident
on it.