DYAL SINGH COLLEGE, UNIVERSITY OF DELHI

(E-RESOURCE MATERIAL / STUDY MATERIAL)

Paper Name: B.Sc, Physical Sciences, Sem- IV, Sec-B,

C Wave and Optics

Teacher’s Name- Dr. Mayuri

MonikaSrivastava
Monika Gupta (Physics Deptt.)
Gupta

Time Schedule- Thursday: 2:30 PM to 4:30 PM

Saturday: 8:30 AM to 10:30 AM

POLARISATION (Part-1)
The phenomenon of restricting the vibration of light in a particular
direction perpendicular to the direction of wave motion is called as
polarisation.
To explain the phenomenon of polarisation let us consider the two
tourmaline crystal with their optics axis placed parallel to each other
.When an ordinary light is incident normally on the two crystal plates
the emergence light shows a variation in intensity as T2 is rotated.
The intensity is maximum when the axis of T2 is parallel to that of T1
and minimum when they are at right angle. This shows that the light
emerging from T1 is not symmetrical about the direction of
propagation of light but its vibration are confined only to a single line
in a plane perpendicular to the direction of propagation, such light is
called as polarised light.
Example:

Difference between Polarised and ordinary light:

Polarised light Ordinary light
1. The vibrations are confined 1. The vibrations of light
in a particular direction. particle are not confined in a
2. The probability of particular direction.
occurrence of vibration 2. The probability of
along the axis of crystal is occurrence of vibration
not same in all position of along the axis of the crystal
crystal is not symmetries for all
3. The intensity of light plate position of the crystal.
is not same in all position of 3. The intensity of light plate
the crystal plate. is same in all position of the
plate.
 Polarised light:
The resultant light wave in which the vibrations are confined in a
particular direction of propagation of light wave, such light waves are
called Polarised light. Depending on the mode of vibration in a
particular direction, the polarised light is three types:-
Linearly Polarised /Plane polarised:
When the vibrations are confined to a single linear direction at right
angles to the direction of propagation, such light is called Plane
polarised light.

Circularly polarised light:

When the two plane polarised wave superpose under certain
condition such that the resultant light vector rotate with a constant
magnitude in a plane perpendicular to the direction of propagation and
tip of light vector traces a circle around a fixed point such light is called
circularly polarised light.
Elliptically polarised light:
When two plane polarised light are superpose in such a way that the
magnitude of the resultant light vector varies periodically during its
rotation then the tip of the vector traces an ellipse such light is called
elliptically polarised light.

Pictorial representation of polarised light:

Since in unpolarised light all the direction of vibration at right angles
to that of propagation of light. Hence it is represented by star symbol.

In a plane polarised beam of light, the polarisation is along straight line,

the vibration are parallel to the plane and can be represented by
If the light particles vibrate along the straight line perpendicular to the
plane of paper, then they can be represented by a dot.

Plane of vibration:
The plane containing the direction of vibration and direction of
propagation of light is called as plane of vibration.

Plane of polarisation:
The plane passing through the direction of propagation and containing
no vibration is called as plane of polarisation.
Since a vibration has no component of right angle, to its own direction,
so the plane of polarisation is always perpendicular to the plane of
vibrations. Angle between plane of vibration and plane of polarisation
is 90˚.
Light waves are transverse in nature:
If the light waves are longitudinal in nature, they will show no variation
of intensity during the rotation of the crystal. Since during the rotation
of the crystal, the variation in intensity takes place, this suggests that
light waves are transverse in nature rather longitudinal.
Production of plane polarised light:
The plane polarised light can be produced in four different ways such
as
1. Polarisation by Reflection
2. Polarisation by Refraction
3. Polarisation by Scattering
4. Polarisation by Double refraction
1. Polarisation by reflection:
The production of the polarised light by the method of reflection from
reflecting interface is called polarisation by reflection.

When the unpolarised light incident on a surface, the reflected

light may be completely polarised, partially polarised or unpolarised
depending upon the angle of incidence. If the angle of incidence is 0°
or 90° the light is not polarised. If the angle of incidence lies in between
0° and 90°, the light is completely plane polarised.
The angle of incidence for which the reflected component of
light is completely plane polarised, such angle of incidence is called
polarising angle or angle of polarisation or Brewster’s angle .It is
denoted by ip.
At ip the angle between reflected ray and refracted or
transmitted ray is π/2.
Explanation: To explain the polarisation by reflection, let us consider
an interface XY on which a ray AB which is unpolarised is incident at
an angle equal to polarising angle and get reflected along BC which is
completely plane polarised and the ray BD which is refracted or
transmitted is continues to be unpolarised. The incident unpolarised
light contain both perpendicular and parallel component of light.
 The parallel component of light is converted into perpendicular
component and gets reflected from the interface. The parallel
component of light is continues to vibrate and get refracted or
transmitted. As a result of which the reflected component is polarised.
Conclusion:
Hence, the reflected ray of light contains the vibrations of electric
vector perpendicular to the plane incidence. Thus the reflected light is
completely plane polarised perpendicular to plane of incidence.
Brewster’s Law:
This law states that when an unpolarised light is incident at polarizing
angle “ip” on an interface separating air from a medium of refractive
index “µ” then the reflected light is fully polarized. i.e.   tan ip
To explain Brewster’s law, let XY be a reflecting surface on which;
AB = unpolarised incident light
BC= completely polarized
BD = partially polarized
ip =angle of incidence, angle of polarization
From fig.

 CBY+  DBY=90˚
900  r  900  r 900
'

 900  ip  900  r 90  0


 ip r  900

 r '  900  r
From Snell’s law
 sin i p = sin i p = sin i p = tan ip
sin r sin(900  i p ) cos i p
Thus the tangent of the angle of polarization is numerically equal to
the refractive index of the medium.
NOTE: We can also prove in case of reflection at Brewster’s angle
reflected and refracted ray are mutually perpendicular to each other.
From Brewster’s law;
We have   tan ip sin ip
cos ip
 According to Snell’s law;
  sin ip
sin r
From above equations
sin r  cos ip sin r  sin(900  i p )  r  900  ip  r  ip 900

  900 CBY  900 DBY  900

  CBY+  DBY=90˚
 CB  BD CBD  900
Thus, it is concluded that at polarizing angle or at Brewster’s angle, the
reflected light and the refracted light are mutually perpendicular to each
other.

2. Polarisation by Scattering:
When a beam of ordinary light is passed through a medium containing
particles, whose size is of order of wavelength of the incident light, then
the beam of light get scattered in which the light particles are found to
vibrate in one particular direction. This phenomenon is called
“Polarisation by scattering”.

Explanation:
To explain the phenomenon of scattering, let us consider a beam of
unpolarised light along z-axis on a scatter at origin. As light waves are
transverse in nature in all possible direction of vibration of unpolarised
light is confined to X-Y plane. When we look along X-axis we can see
the vibrations which are parallel to Y-axis. Similarly, when we look
along Y-axis the vibration along X-axis can be seen. Hence, the light
can be scattered perpendicular to incident light is always plane
polarized.

Polarisation by refraction:
The phenomenon of production of polarised light by the method
of refraction is known as polarisation by refraction.
To explain the polarization by refraction, let us consider an ordinary
light which is incident upon the upper surface of the glass slab at an
polarizing angle i p or Brewster’s angle B , so that the reflected light is
completely polarized while the rest is refracted and partially polarized.
The refracted light is incident at the lower face at an angle “r”.
Now,
sin r sin r sin r
tan r    g a tanrga
cos r sin(90 0  r) sin i p

Thus according to Brewster’s law, “r” is the polarizing angle for the
reflection at the lower surface of the plate. Hence, the light reflected at
the lower surface is completely plane-polarised, while that transmitted
part is partially polarised. Hence, if a beam of unpolarised light be
incident at the polarizing angle on a pile of plates, then some of the
vibrations are perpendicular to the plane of incidence are reflected at
each surface and all those parallel to it are refracted. The
net result is that the refracted beams are poorer and poorer in the
perpendicular component and less partially polarised component.

Malus’ law:
It states that when a beam of completely plane polarized light
incident on the plane of analyser, the intensity of the transmitted light
varies directly proportional to the square of the cosine of the angle
between the planes of the polariser and plane of the analyser.
Mathematically,
I cos 2 
Proof:
Let us consider a beam of plane polarised light coming from the plane
of the polariser is incident at an angle “” on the plane of the analyser.
The amplitude of the light vector “E” is now resolved into two mutual
perpendicular component i.e. E1  E0 cos which is parallel to the plane of
transmission and E2  E0 sin which is perpendicular to the plane of
transmission. As we are able to see only the parallel component so the
intensity of the transmitted light coming from the plane of the analyser
is proportional to the parallel component only.
Thus,
IE 2  I  kE2 cos 2   I cos 2  , where I  kE2
1 0 0 0 0

I cos2 which is Malus’s law

Double refraction:
The phenomenon of splitting of ordinary light into two refracted ray
namely ordinary and extra ordinary ray on passing through a double
refracting crystal is known as double refraction
Explanation:
To explain the double refraction, let us consider an ordinary light
incident upon section of a doubly refracting crystal

When the light passing through the crystal along the optic axis then at
the optic axis the ray splits up into two rays called as ordinary and
extraordinary ray which get emerge parallel from the opposite face of
the crystal through which are relatively displaced by a distance
proportional to the thickness of the crystal. This phenomenon is called
as double refraction.
Difference between ordinary (O-ray) and Extra ordinary ray (E-
ray)

Ordinary ray Extra Ordinary ray

1.These ray obeys the law of 1. These ray do not obey law of
refraction
2.For ordinary ray refraction
plane of vibration lies 2.For extraordinary ray the
perpendicular to the plane of vibration parallel to
direction of
propagation the direction of propagation

3. The vibration of particle is

3.The vibration of particles are parallel to the direction of ray.
perpendicular to the
direction of ray. 4. Plane of polarisation is
4. Plane of polarisation lies in perpendicular to
the its principal axis.
principal plane. 5. Refractive index varies along
5. Refractive index is constant Optics axis.
along
optics axis. 6.It travels with different speed
6. It travels with the constant in different direction .But it
speed in all direction. travel with equal speed along
optics axis
Double refracting crystal:
The crystal which splits a ray of light incident on it into two refracted
rays such crystal are called double refracting crystal.It is of two types
1. Uniaxial
2. Biaxial.
Uniaxial: The double refracting crystal which have one optic axis
along which the two refracted rays travel with same velocity are
known as uniaxial crystal
Ex: Calcite crystal, tourmaline crystal, quartz
Biaxial: The double refracting crystal which have two optic axis
are called as biaxial crystal
Ex: Topaz, Agromite
Optic axis: It is a direction inside a double refracting crystal along
which both the refracted behave like in all respect.
Principal section: A plane passing through the optic axis and normal
to a crystal surface is called a principal section
Principal plane:
The plane in the crystal drawn through the optic axis and ordinary ray
or drawn through the optic axis and the extraordinary ray is called as
principal plane these are two principal plane corresponding to refracted
ray.
Polarisation by double refraction:
To explain polarisation by double refraction let us consider a beam of
light incident normally through a pair of calcite crystal and rotating the
second crystal about the incident ray as axis we have the following
situations as:
Case 1
When principal sections of two crystals are parallel then two images
O1 and E1 are seen. The ordinary ray from the first crystal passes
undeviated through the 2nd crystal and merges as O1 ray. The
extraordinary ray (E-ray) from the 1st crystal passes through the 2 nd
crystal along a path parallel to that inside the 1st and emerges as E1-
ray. Hence the image O1 and E1 are seen separately.
 Case 2
When the 2nd crystal is rotated through an angle 45˚ with respect to 1 st,
then the two new images O2 and E2 appear. As the rotation is continued,
O1 and O2 remained fixed while E1 and E2 rotate around O1 and O2
respectively and images are found to be equal intensities.
Case 3
When the 2nd crystal is rotated at an angle 90˚ w.r.t 1st the original images
O1 and E1 have to vanish and all the new images O2 and E2 have acquired
the maximum intensity.

When the 2nd crystal is rotated at an angle st
 135˚ w.r.t the 1 , four images
once
 again appear with equally intense.

When the 2nd crystal is rotated at an angle 180˚ w.r.t 1 st, the O2 and E2

vanishes and O1 and E1have come together in the centre.

This is how we are able to produce the plane polarised light by the
method of double refraction.