Polarisation

Polarisation
Only transverse waves can be polarised. Therefore, the fact
that light waves can be polarised is a proof that EM waves are
transverse in nature.

Imagine a rope and you
are moving it in xz
plane and then
in yz plane.
It can be related to
plane polarised light in
x- direction if Electric
filed is oscillating in xz
plane

What if you start
moving this rope in
a circle.
It can be related to
circularly polarised
light .

What if you start moving rope in random directions in
short interval of time?
It can be related to unpolarised light.

What if you introduce a slit in the path?
If a longitudinal wave were propagating in string, amplitude
of transmitted wave would have been same for all
orientations.

Electromagnetic Waves :
The direction of polarisation of an electromagnetic wave has
traditionally been defined to lie along the direction of oscillation
of the electric field.

P1 and P2 are polaroids.
If P1 and P2 are
parallel to each other,
light intensity will be
maximum
after P2.
If P1 and P2 are
perpendicular to each
other, light intensity is
minimum after P2.

Representation of unpolarised light:
Electric field vector is decomposed into 2 perpendicular
components. If direction of propagation of wave is z-direction,
then Electric field vector is decomposed into x and y
components.
For unpolarised light, the components have equal amplitudes,
and the phase difference between them varies randomly.

Direction of
propagation
Represents component out of plane
Represents component in the plane
Direction of
propagation
If E is represented in x and y direction:

Production of Linearly Polarised light:
● The wire grid polariser
● The Polaroid.
● Polarisation by reflection.
● Polarisation by double refraction.

➢ Very thin Copper wires placed parallel to each other.
➢ When an unpolarised light is incident on it, component
of electric vector along the length of the wire is
absorbed. Because electrons in wire start moving in
electric field and energy associated with electric field is
lost in Joule heating of wires.
➢ Since wires are very thin electric field component along
the x-axis passes through without much attenuation
because electrons don't have much space to move.
➢ Therefore, outgoing wave is linearly polarised with
electric vector in x-direction.

It will work ( Ey will be almost completely attentuated) if the
spacing between is ≤λ.
Therefore, this polariser is easy to fabricate for a 3cm
microwave because spacing needed between wires ≤3 cm.
Visible light waves have small wavelength (5 × 10-5
cm),
fabricating a polariser with wire spacing ≤ 5 × 10-5
cm is
very difficult. A polaroid is used for this.

Polaroids:
➢ Instead of Cu wires, long chain polymer molecules
that contain atoms (such as iodine) which provide high
conductivity along the length of the chain.
➢ These long chain molecules are aligned so that they
are almost parallel to one another.
➢ Because of the high conductivity provided by the
iodine atoms, the electric field parallel to the molecules
gets absorbed.
➢ A sheet containing such long chain polymer molecules
(which are aligned parallel to one another) is known as
a Polaroid.

When a light beam is incident on such a Polaroid, the
molecules (aligned parallel to one another) absorb the
component of electric field which is parallel to the direction
of alignment because of the high conductivity provided by
the iodine atoms; the component perpendicular to it
passes through.
Thus the aligned conducting molecules act similar to the
wires in the wire grid polarizer, and since the spacing
between two adjacent long chain molecules is small
compared to the optical wavelength, the Polaroid is usually
very effective in producing linearly polarized light

If you start rotating the analyser, at 90o
and 270o
, the
transmitted intensity will be minimum.
The transmitted intensity will be maximum when analyser
is at angle of 0o
and 180o
.
The lines show the direction of polarisation.

Polarisation by Reflection:
Brewster discovered that there is a particular angle of
incidence at which, if unpolarised light is incident on glass
or dielectric material, the reflected light is polarised.
This particular angle of incidence is also known as
Brewster angle and is given by :
Using a polaroid, reflected light can be checked for
polarisation. Intensity of reflected light should be zero
twice in one complete rotation.
θ=θp=tan−1
(
n2
n1
)

If an unpolarized light is incident at Brewster angle, then
the reflected beam will be linearly polarized with its electric
vector perpendicular to the plane of incidence.
Air
Glass
Unpolarized light
Reflected
polarized light
θp θp
θr

Air
Glass
polarized wave
No reflected
wave
θp
θr
If an wave polarised in plane of paper is incident at Brewster
angle, then there will be no reflected beam!

θp=tan−1
(
n2
n1
)Brewster angle is given by :
If wave is incident from air to glass, n1
= 1. Therfore,
θp=tan−1
(n2)⇒ tan(θp)=n2
sin(θp)
cos(θp)
=n2
Applying Snell's law :
sin(θp)
sin(θr)
=n2
From both of these equations:
sin(θp)
sin(θr)
=
sin(θp)
cos(θp)
⇒sin(θr)=cos(θp)
⇒sin(θr)=sin(90o
−(θp))
⇒θr=90
o
−θp ⇒θr+θp=90
o

Air
Glass
Unpolarized light
Reflected
polarized light
θp θp
θr
90o

Intensity of reflected polarised light can be increased by
using a pile of plates.

Polarisation by double refraction :
● If beam of light is passed through certain crystal like
calcite (CaCO3
) or quartz (SiO2
), it splits into two beams.
These substances are called doubly refracting or
birefringent.

One of refracted beams obeys Snell's law and is called
Ordinary ray (O-ray). The other beam doesn't obey
Snell's law and is called Extraordinary ray (E-ray).

● The E-ray travels in the crystal with a speed that varies
with direction and is described by ellipsoid. The O-ray
travels in the crystal with a constant speed in all
direction and is described by spheroid.
● The refractive index for O-rays is constant and is
direction dependent for E-rays.
● In the case of Calcite and Quartz crystal, there is one
direction in which there is no double refraction. This
direction is called optic axis or principal axis. There
are also biaxial crystals, no double refraction occurs in
two specific directions.
● O-rays and E-rays are polarised in a direction
perpendicular to each other. O-rays are polarised
perpendicular to plane containing optical axis.

The optic axis of a calcite crystal denoted by dotted line
AB. Any ray of ordinary unpolarised light incident along the
optic axis or parallel to this axis does not split up into two
rays.

The plane containing the optic axis and the perpendicular
to the pair of opposite faces of the crystal is known as
principal section for that pair of faces of the crystal.
Since the crystal has six faces, for each pair of opposite
faces of the crystal, there are three principal sections.

S is the point from where light is starting at same
time in double refracting crystal.
Wavefront of O- and E-rays :

For negative uniaxial crystals (like calcite) in which the
velocity of O-ray is less than the velocity of E-ray, sphere
lies inside the ellipsoid. However, for positive uniaxial
crystals (like quartz) the ellipsoid lies inside the sphere
since in this case the velocity of O-ray is greater than the
velocity of E-ray.
Negative crystal
Vo
<Ve Vo
> Ve
S
Optic axis e wavefronto wavefront
Vo
Ve
Positive crystal

Nicol Prism : Based on double refraction
Nicol prism is an optical device which is used for
producing and analyzing plane polarized light in practice.
Calcite crystal is cut along a diagonal and cemented back
together with special cement called Canada balsam.
o
= 1.65836, canada balsam
= 1.55, e
= 1.48641
Birefringence (B) = |e
- o
|
where e
and o
are the refractive indices experienced by
the extraordinary and ordinary rays, respectively.

Its end faces PQ and RS are cut such that the angles in
the principal section become 68° and 112° in place of 71°
and 109° ( naturally occurring crystal).
Length three times of its width

Working of Nicol Prism :
➢ When a beam of unpolarised light is incident on the face
P′Q, it gets split into O-ray and E-ray.
➢ These two rays are plane polarised rays, whose
vibrations are at right angles to each other. The refractive
index of Canada balsam cement being 1.55 lies between
those of ordinary and extraordinary (1.65836 and 1.4864,
respectively).
➢ Canada Balsam layer acts as an optically rarer medium
for the ordinary ray and it acts as an optically denser
medium for the extraordinary ray.

➢ When ordinary ray of light travels in the calcite crystal
and enters the Canada balsam cement layer, it passes
from denser to rarer medium. Moreover, the angle of
incidence is greater than the critical angle, the incident
ray is totally internally reflected from the crystal and only
extraordinary ray is transmitted through the prism.
➢ Therefore, fully plane polarised wave is generated with
the help of Nicol prism.

Nicol Prism as a Polariser and an Analyser :
➢ In order to produce and analyse the plane polarised light,
two nicol prisms are arranged.
➢ When a beam of unpolarised light is incident on the nicol
prism, emergent beam from the prism is obtained as plane
polarised, and which has vibrations parallel to the principal
Section.
➢This prism is therefore known as polariser. If this polarised
beam falls on another parallel nicol prism P2, whose
principal section is parallel to that of P1, then the incident
beam will behave as E-ray inside the nicol prism P2 and
gets completely transmitted through it.
➢ This way the intensity of emergent light will be maximum.

➢ Now the nicol prism P2 is rotated about its axis, then we
note that the intensity of emerging light decreases and
becomes zero at 90° rotation of the second prism (Fig. b).
➢ In this position, the vibrations of E-ray become
perpendicular to the principal section of the analyser (nicol
prism P2).
➢ Hence, this ray behaves as O-ray for prism P2 and it is
totally internally reflected by Canada balsam layer. This
fact can be used for detecting the plane polarised light and
the nicol prism P2 acts as an analyser.
➢ If the nicol prism P2 is further rotated about its axis, the
intensity of the light emerging from it increases and
becomes maximum for the position when principal section
of P2 is again parallel to that of P1 (Fig. c). Hence, the
nicol prisms P1 and P2 acts as polariser and analyser,
respectively.

Malus' law :
polarizer P1
which has a pass axis parallel to the y axis;
i.e., if an unpolarized beam propagating in the z direction
is incident on the polarizer, then the electric vector
associated with the emergent wave will oscillate along the
y axis.
y

Consider the incidence of the y-polarized beam on the
Polaroid P2
whose pass axis makes an angle θ with the y
axis. If the amplitude of the incident electric field is E , then
the amplitude of the wave emerging from the Polaroid P2
will be E cos(θ),
Only Ey
will be transmitted, Ex
will be absrobed.
Ey
=E0
cosθ
Remember lines here show
direction of polarisation not wire
grid or chain molecules direction.
Here, wire grid or chain molecules
are aligned along x-axis.

The intensity of the emerging beam will be given by
I = I0
cos2
(θ) Malus' law
where I0
represents the intensity of the emergent beam
when the pass axis of P2
is also along the x axis (i.e., when
θ = 0).

Anti-glare automobile headlights :
45o
45o
Two approaching vehicles
Wind screen
Head light
The transmission or pass
axis shown by lines in head
light and wind screen are
perpendicular to each other.
No light from the head light
will pass through the
Wind screen.

Adjustable tint windows :
By adjusting relative orientation of 2 polaroids, the light
intensity is adjusted in tint windows.

Polarisation

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