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Electromagnetic Wave
In 1864 James Clerk Maxwell proved that the light wave is an electromagnetic wave. In
electromagnetic wave the electric field and magnetic field vectors are perpendicular to each other
and vary simple harmonically in same phase in the plane perpendicular to the direction of
propagation of wave as shown in figure. Thus, the electric field vectors, magnetic field vectors and
direction of propagation of wave all the three are perpendicular to each other, that is light waves are
transverse in nature.
E (Electric field vector)
Direction of propagation
B (Magnetic field vector)
The plane in which the electric field vector and the direction of propagation of wave exist is known
as plane of vibration i.e. X-Z plane and the plane perpendicular to the plane of vibration in which
components of electric field are zero but contains the direction of propagation is known as plane of
polarization i.e. Y-Z plane.
Polarization of Light, Polarized and Unpolarized Light
The emission of light is due to transition of electrons from excited states to lower states. The light
ray made up of a very large number of electromagnetic waves in which electric field vectors of
different waves vibrate in all possible direction perpendicular to the direction of propagation of
light. Such light ray is called unpolarized light. If the direction of propagation is taken normal to
the paper, then unpolarized light can be shown according to fig.
X
Z
Y
If the vibrations of the electric field vector are confined in a definite direction or definite plane,
then this state of light is called polarized light and the phenomenon is called polarization of light.
The plane in which the electric field vector and the direction of propagation of wave exist is known
as plane of vibration i.e. ABCD plane and the plane perpendicular to the plane of vibration in
which components of electric field are zero but contains the direction of propagation is known as
plane of polarization i.e. EFGH plane.
Plane, Circularly & Elliptically Polarized light(On the basis of electricvector):
(1) Plane Polarized Light (PPL)
If the vibrations of the electric field vector (light vectors) are confined in a definite direction or
plane, then that type of light is called plane polarized light.
In plane polarized light, the light vector vibrates simple harmonically along a fixed single plane
perpendicular to the direction of propagation and orientation of light vector remains unchanged
with respect to time.
rotates in an elliptical path, then that type of light is called elliptically polarized light. It can be
represented as:
Double Refraction; Qualitative Description:
When a light ray is incident upon the certain crystals such as Calcite, Iceland-Spar, the ray splits
into two refracted rays due to refraction. This phenomenon is called double refraction or
bifringence and crystal is called double refracting crystal. The refracted rays are two types:
1. Ordinary Ray (O-Ray)
The refracted ray, obeys general laws of refraction (Snell’s Laws) and always remains in the same
plane of incident ray is called O-Ray. The velocity of O-Ray in crystal is found same in all
directions.
2. Extraordinary Ray (E-Ray)
The refracted ray, does not obey general laws of refraction (Snell’s Laws) is called E-Ray. The
velocity of E-Ray in crystal is found different in all directions.
(UPL)
E-rays and O-rays both are plane polarized light and vibrations of these rays are perpendicular to
each other. In O-ray the direction of vibrations of electric field vector are perpendicular to the plane
while in E-ray the vibrations of electric field vector are parallel to the plane as shown in figure.
E
A B
O
E-Ray
O-Ray
Optic Axis and Principal Section of the Crystal
The structure of calcite crystal is parallelogram whose angles are 1 02
o and 78
o
. There are two
opposite corners D & F where the intersecting edges enclose three equal obtuse angles of 102
o .
These corners are called blunt corners. At the remaining six corners (A,B,C,E,G and H); one angle
is obtuse (
o ) and two are acute ( 78
o ).Fig ( a )
A line passing through anyone of the blunt corners (D or F) and equally inclined to the three faces
meeting there, represent the optic axis of the crystal i.e. OO. And the crystal is symmetric about
this axis and velocities for E-ray & O-Ray in crystal are same along optic axis. Optic axis is not a
line but it is a direction. All imaginary lines parallel to this direction will be the optic axis of the
crystal.
A plane containing the optic axis and perpendicular to the two opposite faces of the crystal is
defined as the principal section of the crystal.
If the crystal structure is such that the edges DA, DC & DH are equal then the line joining the
points D and F i.e. DF line represents the optic axis and plane ADGF represents the principal
section of the crystal. Fig ( b )
If unpolarized light is made to incident on such a crystal, then only those vibrations of electric
vector which are parallel to the optical axis will be able to pass through the crystal (emergent light
being plane polarized) and vibrations in all directions will be absorbed.
Fig (a)
Fig (b)
A B
C
H G
O
D
E
F
o
o
o
o
o 102
o
O
Optical Axis
Case II: If = /2 or 90
o , then cos
2 = 0, Hence I = 0
Thus when planes of transmission of polarizer and analyzer are perpendicular to each other, no
light is transmitted through the analyzer.
Case III: If an unpolarized light is incident on the polarizer, in that case the intensity of light
transmitted by the polarizer is one-half the intensity of unpolarized light incident on it.
Proof: Let us consider be the angle between the plane of vibration of the electric vector of the
incident light and the plane of transmission of the polarizer.
By Malus law, the intensity of light transmitted by the polarizer will be:
I 0 = Iu cos 2 … (1)
As the incident light is unpolarized, its electric vector vibrates randomly in all directions from = 0
to = 2, thus the intensity of light transmitted through the polarizer will be the average of
equation (1).
I 0 = < I 0 > = Iu< cos
2 >
But < cos 2 > = ½
Thus the intensity of light transmitted through the analyzer is given by:
2 cos 2
I u I
where, Iu is the intensity of incident unpolarized light.
Phase Retardation Plate:
A double refracting crystal plate of uniform thickness, whose refracting surfaces are parallel to its
optic axis and produces as definite phase or path difference between the ordinary and extraordinary
rays is called phase retardation plate.
When a plane polarized light is incident normally on the refracting surface parallel to optic axis, it
splits into E-ray and O-ray. Both waves travel in the same direction but with different speeds. In
calcite crystal the velocity of E-ray is greater than that of velocity of O-ray i.e. V E >V O. So the
difference in time taken by these waves to cross the plate will be:
O E
d d t v v
where, d is the thickness of the plate.
So path difference between the E-ray and O-ray
x = d ( O – E )
where, O and E are the refractive indices of calcite plate for O-ray and E-ray respectively.
Hence the phase difference between the E-ray and O-ray:
x
O E
d
where, is the wave length of incident light this represent the relative phase retardation between
the E-Ray and O-Ray.
There are two types of phase retardation plate:
1. Quarter Wave Plate (QWP)
A double refracting crystal plate of uniform thickness produces a path difference of λ/4 or phase
difference of π/2 between the O-ray and E-ray is called quarter wave plate.
For quarter wave plate in general path difference
n
where, n = 0, 1, 2, 3, …
from equation (1)
2 O E
n d
Half wave plate is used for changing the direction of plane of vibration of the plane polarized
light.
When a plane polarized light is incident normally on the half-wave plate. The emergent ray is also
plane polarized but the plane of vibration of emergent ray rotates through an angle 2 from the
plane of vibration of incident ray. where is the angle between the plane of vibration of the
incident light and the optic axis of the half wave plate.
Half wave plate can change left-handed elliptically or circularly polarized light into respective right
handed elliptically or circularly polarized light.
Optical Activity or Rotatory Polarization:
When a plane polarized light passes through a certain optically active substance, then its plane of
polarization of the emergent light rotates by a definite angle. This phenomenon of rotation of plane
of polarization of plane polarized light about its direction of propagation is called “ optical
activity ”. This phenomenon can be seen in the following figure:
Fig (a): without optically active substance
S
Polarizer (P) Analyzer (A)
No Light
UPL
In this arrangement, an unpolarized light from a source S is passed through the polarizer and
analyzer which are in crossed (Perpendicular) position i.e. the principal sections of polarizer and
analyzer are perpendicular to each other. In this case the intensity of light emerging from analyzer
will be zero i.e. no light is seen through the analyzer. Fig (a)
Now if an optically active substance (such as sugar, quartz, d-glucose, -fructose etc.) whose axis
is perpendicular to the refracting face, is placed in between polarizer and analyzer, in this case the
intensity of light emerging from analyzer will not be zero i.e. some light is seen through the
analyzer. Fig (b)
Fig (b): with optically active substance
From above figure it is clear that optically active substance rotates the plane of polarization of
plane polarized light by a definite angle. This phenomenon is called optical activity, and if any
substance (such as glass, water etc.) does not rotate the plane of polarization of PPL, then that type
of substances are called optically inactive substances.
According to the rotation of plane of polarization, optically active substances are of two types.
(i) Dextrorotatory or Right handed
Those substances which rotate the plane of polarization of plane polarized light in the clockwise
direction are called dextrorotatory substances. e.g. Sugar, d-glucose, camphor, quartz (R) etc.
(ii) Laevorotatory or Left handed
Those substances which rotate the plane of polarization of plane polarized light in the anticlockwise
direction are called Laevorotatory substances. e.g. Turpentine oil, -fructose, quartz (L) etc.
Laws of Optical Activity or Rotatory Polarization
According to biot following laws for Optical Activity:
- The angle of rotation () of plane of polarization of plane polarized light (PPL) of definite
wavelength () is directly proportional to the distance ( l ) traveled by the polarized light in
optically active substance (solid, liquid, gas or solution) i.e.
l
- The angle of rotation () of plane of polarization of plane polarized light (PPL) of definite
wavelength () is directly proportional to the concentration (c) of the solution or vapour (only
for dilute solutions) i.e.
c
plate will introduce a phase difference of (path difference of /2) between the ordinary and extra
ordinary ray.
The thickness of the glass plate is adjusted such that it transmits the same amount of light as
transmitted by quartz plate. This type of circular plate is called Laurent’s half shade device.
(ii) Construction:
Laurent’s half shade (wave) polarimeter has a sodium light or monochromatic light source. In this
polarimeter a half shade device is placed in between polarizer and glass tube to increase its
sensitivity. Polarizer is a Nicol prism which is kept in between the convex lens and half shade
device and it is used to polarize the unpolarized light. An optically active solution whose angle of
rotation of plane of polarization is to be measured is kept in a glass tube (kept in between half shade
device and an analyzer). Both ends of the glass tube are covered with two parallel glass plates. The
middle portion of the glass tube has a larger diameter for air bubble if any so that it will not come in
the way of light. An analyzer which is kept in between glass tube and eye piece is also a Nicol
prism and can be rotated about the incident light. Its angular position can be determined by a
circular scale with a vernier attached with the analyzer. Through the eye piece we can see the light
transmitted through the analyzer.
(iii) Working
Light from a monochromatic source or sodium lamp S is incident on the convex lens then it passes
through Nicol Prism (polarizer) and we get plane polarized light. Now this PPL is incident
normally on the half shade device. Let the plane of vibration is in OP direction, then plane of
vibration is transmitted in the same direction OP without any rotation when it passes through
semicircular glass plate and when it passes through semicircular quartz plate (HWP), the beam
splits up in to ordinary and extraordinary rays (O-rays and E-ray) and transmitted through the plate
with a phase difference of π i.e. in the direction OQ. So we can say that two plane polarized light
ray having vibrations along OP and OQ are obtained by transmission through half shade device.
These vibrations are studied using analyzer in the following manner.
Case: I When the principal section A 1 OA 2 of the analyzer is perpendicular to AOB then complete
circular portion (both half portions) will be seen equally bright because OE 1 = OE 2 .Fig.(a).
Case: II When the principal section A 1 OA 2 is rotated clockwise then OE 2 > OE 1 , so left half will
appear brighter than the right half. Fig.(b).
Case: III When the principal section A 1 OA 2 is rotated anticlockwise then OE 1 > OE 2 , so right half
will appear brighter than left half. Fig.(c).
(iv) Determination of Specific Rotation:
For determination of specific rotation first we determine the angle of rotation with the help of
polarimeter. For this the analyzer is rotated to such an extent both halves may appear equally
bright. We set this position firstly for water and then optically active solution in the polarimeter
tube and take the difference of two readings to get angle of rotations. Now the specific rotation can
be determined using following relation.
S =
LC
θ degree/decimeter gm/cm 3
where, = angle of rotation, L = length of polarimeter tube and C = concentration of the solution
(v) Defect
Laurent’s half shade polarimeter can be used only for that wavelength, for which half shade device
acts as a half wave plate (HWP). In general this is used with sodium light or monochromatic light.
TUTE SHEET- 2
- An optical rotation of 8 o occurs when plane polarized light is sent through certain length of
3% solution of glucose. If polarized light is sent through 6% solution of glucose, what
length of solution is needed to produce an optical rotation of 10 o
. (5/8 of previous length)
- A sugar solution in a glass tube of 20 cm length produces an optical rotation of 13 o . The
solution is then diluted to one- third of its previous concentration. Estimate the optical
rotation produced by a 30 cm long glass tube containing the diluted solution. (6. o )
- 80 gm of impure sugar when dissolved in a litre of water, gives an optical rotation of 9.
o ,
when placed in a tube of length 200 mm. If the specific rotation of sugar is 66
degree/dm/(gm/cc), find the percentage purity of sugar sample. (93.75%)
- If 20 cm length of a certain solution causes right handed rotation of 42 o and 30 cm of
another solution cause left handed rotation of 27 o
. What optical rotation will be caused by
30 cm length of a mixture of the above solution in the volume ratio 1 : 2. The solutions are
not chemically reactive. (+ o )
- A 20 cm long tube containing sugar solution rotates the plane of polarization by 11
o
. If
specific rotation of sugar is 66
o /dm/gm/lit. Calculate the strength of solution.
(0.0833gm/cm 3 )
- A 20 cm tube contains sugar solution made by dissolving 15 gm of sugar in 100 cm 3 of
water. What is the angle of rotation of the plane of vibration of a plane polarized light
passing through this tube? Specific rotation of sugar is 66. o (decimeter)
