B.

TECH I SEMESTER ENGINEERING PHYSICS-UNIT I

1.3 POLARISATION
1.3.1 INTRODUCTION:
Polarization is a property of waves that describes the orientation of their plane of vibrations.
Light waves are transverse electromagnetic waves. The electric and magnetic field vibrations are
always perpendicular to the direction of propagation. However, in general the electric field
vibrations are spread in all possible directions but still perpendicular to the direction of
propagation. Getting only one kind of vibration of light from ordinary light is called polarization.
Representation of various types of light:
1. Unpolarised light:
The ordinary light also called as unpolarised light, consists of a very large number of
vibrations in all planes with equal probability at right angles to the direction of propagation.
Hence, the unpolarised light is represented by a star as shown in fig. 3.1.

Fig. 3.1
2. Plane polarised light:
We know that in plane polarised light the vibrations are along a straight line. If the direction
of vibrations is parallel to the plane of paper, it is represented by a straight line arrow as
shown in fig. 3.2 (A). If the direction of vibration is perpendicular to the plane of paper, it
is represented by a dot as shown in fig. 3.2 (B).

Fig. 3.2
1.3.2 PLANE OF POLARISATION:
When ordinary light is passed through a tourmaline crystal, the light is polarized and the
vibrations are confined only in one directions which is perpendicular to the direction of
propagation of light. Now, we consider the case of two planes: Firstly, the plane in which the
vibrations of polarized light are confined. This plane is known as plane of vibrations as shown in
figure…This plane contains the direction of vibrations as well as the direction of propagation.
Secondly, the plane which has no vibrations. This plane is known as plane of polarization as shown
in Fig. 3.3.

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Thus, a plane passing through the direction of propagation and perpendicular to the plane
of vibration is known as plane of polarization.
1.3.3 TYPES OF POLARIZATIONS:
The polarization of light can be classified into three types. They are
1. Plane polarization
2. Circular polarization
3. Elliptical polarization.
1.3.3.1. Plane polarization:
When the light wave propagates through any medium, if the electric component of light
passing through the medium vibrates only along a single direction perpendicular to the direction
of propagation, the wave is said to be plane polarized or linearly polarized.
The resultant electric vector E can be resolved into two rectangular components Ex and Ey.
Thus the transverse electric vector may be regarded as superposition of two mutually perpendicular
electric fields.
Hence E= Ex + Ey. E is linearly polarized if two electric vectors are mutually perpendicular
with zero phase difference superimpose, the magnitude of the resultant vector E remain linear
between X and Y directions during the course of propagation.

1.3.3.2. Circular polarization:

When two coherent light waves of equal magnitudes and the electric vectors E mutually
perpendicular to each other superimpose, the magnitude of the resultant vector E remain constant,
but it rotating about the axis of direction of propagation such that it goes on sweeping a circular
helix in space during the propagation. Such light wave is called circularly polarized light. If we
imagine that we are looking into the light vector E, we observe that the tip of light vector E traces
a circle on the plane perpendicular to the ray direction. If rotation of the vector tip is clockwise,

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the light is said to be right circular polarized or the tip is rotating anticlockwise, the light is said to
be left circularly polarized.

1.3.3.3. Elliptical polarization:

When two coherent light wave of unequal magnitudes and different in phase superimposed,
the magnitude of the electric vectors E changes with time and rotating about the axis of direction
of propagation. The tip of the electric vector E sweeps a flattened helix in space and traces an
ellipse in a plane perpendicular to the direction of propagation, such light is called elliptically
polarized light.

1.3.4 METHODS OF POLARISATION:

Following are the methods used for producing plane polarised light:
1. Polarisation by reflection.
2. Polarisation by refraction.
3. Polarisation by double refraction.
4. Polarisation by selective absorption.
5. Polarisation by scattering.
1.3.4.1 Polarisation by Reflection (BREWSTER’S LAW):
The simplest way of producing a plane polarised light is by reflection. In 1808, Malus
discovered that when ordinary light is reflected from the surface of a transparent medium like glass
or water it becomes partly polarised. The degree of polarisation changes with the angle of
incidence. At a particular angle of incidence the reflected light has the greatest percentage of
polarised light. The angle depends upon the nature of the reflecting surface. The angle of incidence
is known as angle of polarisation.
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In 1811, Brewster performed a number of experiments to study the polarisation of light by

reflection at different surfaces. He observed that for a particular angle of incidence known as angle
of polarisation, the reflected light is completely polarised in the plane of incidence. i.e., having
plane of vibrations perpendicular to the plane of incidence.
Brewster proved that the tangent of the angle of polarisation is numerically equal to the
refractive index of the medium, i.e.,
µ = tan p
This is known as Brewster’s law. He also proved that the reflected and refracted rays are
perpendicular to each other.
Angle between reflected and refracted rays:
Suppose a beam of unpolarised light is incident on glass surface at polarising angle p as
shown in fig. 3.7. The polarising angle for air glass is 57°. A part of incident light is reflected while
a part is refracted. Let r be the angle of refraction. From Brewster’s law,
µ=tan p …(1)
from Snell’s law,
µ =sin p/sin i …(2)
comparing eqn. 1 and eqn. 2,
tan p = sin p/sin i
sin p/cos p = sin p/sin r
sin r = cos p= sin (90°-p)
r = 90°-p
r + p = 90°
Therefore the reflected and refracted rays are at right angles to each other. Here, it should
be noted that the refracted index of a substance varies with wavelengths. Therefore, for complete
polarisation the light should be monochromatic.

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1.3.4.2 Polarisation by Refraction - Pile of Plates:

When ordinary light (unpolarised light) is incident on the upper surface of the glass slab at
polarising angle, a small fraction is reflected and rest is refracted. The reflected light is completely
plane polarised with vibrations perpendicular to the plane of incidence as shown in fig…The
reflected light is partially polarised having vibrations both in the plane of incidence as well as
perpendicular to the plane of incidence.

In order to make the refracted light to be completely plane polarised light, a pile of glass
plates is used. A pile of plates consists of about 9 or 10 glass plates arranged one above the other
as shown in fig. 3.9.
The ordinary light is incident on pile of plates at polarising angle, a few vibrations
perpendicular to the plane of incidence are reflected by the first plate and rest are refracted through
it. When this beam of light is reflected by the 2nd plate, again some vibrations perpendicular to the
plane of incidence are reflected by this plate and rest are transmitted.
It is important to mention here that each time, the light is incident on the surface of glass
plate at Brewsters angle. The above procedure continues for different glass plates. At the last plate
we get almost plane polarised light with vibrations parallel to the plane of incidence. So, the
reflected light is plane polarised light.
1.3.4.5 Scattering of light and polarisation by scattering:
When a light wave travelling in space, it strikes an extremely small particle (compared to
the wavelength of light) such as dust particle, water particle or molecules of a substance. Now a
portion of the light is scattered by the particle. When the light passes through a number of particles,
its intensity goes on decreasing due to scattering.
According to the Lord Rayleigh, the intensity of scattered light is:
1. Proportional to the intensity of incident light.
2. Proportional to the square of the volume of scattered particles, and
3. Inversely proportional to the fourth power of the wavelength of light used. i.e., I ∝ (1/λ4)
It has been observed that the scattered light is polarised fully or partially depending on the
size of scattering particle. When the size of the particle is sufficient small, the scattered light is
fully polarised while when the particles are larger, the scattered light is partially polarised.

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1.3.6 MALUS LAW:

According to the Malus, when a completely plane
polarised light beam is incident on the analyser, the
intensity of the polarised light transmitted through the
analyser varies as the square of the cosine of the angle
between the plane of transmission of the analyser and
plane of the polarizer.
This law holds good for the combination of the
reflecting surfaces, polarising and analysing tourmaline
crystals, Nicol prisms etc., but fails when the light is not
completely plane polarised.
To prove this, let OP = a be the amplitude of the incident plane polarised light from the
polarizer and θ, the angle between the planes of polarizer and analyser. The amplitude of the
incident plane polarised light can be resolved in two components, one parallel to the plane of
transmission of analyser (a cos θ) and the oter perpendicular to it (a sin θ). The component a cosθ
is transmitted through the analyser.
Therefore Intensity of the transmitted light through the analyser
I   a cos    a 2cos 2
2

intensity ∝ ( amplitude)2
If I be the intensity of incident polarised light then,
I = a2
I  I cos 2
I  cos 2
When θ = 0 i.e., the two planes are parallel so Iθ =1 as cos θ =1
When θ = π/2 i.e., the two planes are perpendicular, Iθ = 0
The above results are experimentally observed in case of two tourmaline crystals.
1.3.7 Geometry of Calcite Crystal:
Calcite crystal is a colourless transparent crystal.
Chemically it is hydrated calcium carbonate (CaCO3). It was
at one time found in great qualities in Iceland and is very large
crystals of waterly clearness. Hence, it is also known as
Iceland spar. It belongs to the rhombo-hedral class of
hexagonal system. The 6 faces of rhombohedron are
parallelograms each having angles of 101° 55’ and 78° 5’ as
shown in fig. 3.11.
There are two opposite corners A and B where the
three obtuse angle (101°55’) meet. The corners are known as
blunt corners. At the rest of six corners there is one obtuse angle and two acute angles.
1. Optic Axis:
A line passing through any of the blunt corners A and B and making equal angles with the
three faces which meet, at this corner, locate the direction of the optic axis of the crystal. It may
be emphasized here that optic axis is a direction and not a particular line. Hence, an optic axis can
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be drawn through every point in the crystal i.e., any line parallel to the line described will be optic
axis.
If the rhombohedron is cut in such a way that its all edges are equal, then the line AB
joining the two blunt corners or any line parallel to this will give the direction of optic axis. Crystals
having one optic axis are called uniaxial crystals and those having two optics axes are called biaxial
crystals (like mica).
2. Principal Section:

Any plane which contains the optic axis and is perpendicular to two opposite faces is called
a principal section. As a crystal has 6 faces, so for every point inside the crystal there are three
principal sections, one for each pair of opposite crystal faces. A principal section cuts the crystal
surfaces in a parallelogram having angle 71° and 109°. In fig the principal sections of the crystal
is shown. An end on view of any principal section is a straight line shown dotted in fig in the
crystal surface parallel to its shorter diagonal CB, which is the end on view of the principal sections
through the blunt edges.
1.3.8 DOUBLE REFRACTION OR BIREFRINGENCE:
The physical properties of refraction in isotropic medium are the same in all directions but
in anisotropic substances (particularly crystalline substance except those having cubic symmetry)
the physical properties are different in different directions. Crystals of calcite, quartz and
tourmaline are well known examples of an isotropic materials.
In 1869, Erasmus Bartholinus discovered that when a beam of ordinary unpolarised
light is passed through a calcite crystal, the refracted light is split up into two rays. The one which
always obey the ordinary laws of refraction and having vibrations perpendicular to the principal
section is known as ordinary ray. The other, in general, does not obey the laws of refraction and
having the vibrations in the principal section is known as extraordinary ray. Both the rays are plane
polarised. This phenomenon is known as double refraction. The crystals showing this phenomenon
are known as doubly refracting crystals.
The phenomenon of splitting of a light ray into rays when it propagates through
homogenous transparent anisotropic medium is called double refraction.

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B.TECH I SEMESTER ENGINEERING PHYSICS-UNIT I

Consider a beam AB of unpolarised light incident on the calcite crystal at an angle of

incident I as shown in fig. Inside the crystal the ray breaks up into orinary and extraordinary rays.
The ordinary ray travelling along BD makes an angle of refraction 𝑟1 while the extra travelling
along BC makes an angle of refraction 𝑟2 . Since, the two opposite faces of the crystals are always
parallel, both the rays emerge parallel to the incident ray. The refractive index of the ordinary and
extraordinary rays can be expressed as
𝑠𝑖𝑛 𝑖 𝑠𝑖𝑛 𝑖
µ0 = 𝑎𝑛𝑑 µ𝑒 = respectively.
𝑠𝑖𝑛 𝑟1 𝑠𝑖𝑛 𝑟2
In the case of calcite µ0 > µ𝑒 because 𝑟1 < 𝑟2 . Therefore, the velocity of light for ordinary
ray inside the crystal will be less than the extraordinary ray. It is observed that the µ 0 is same for
all the angles of incidence while µe varies with angles of incidence. Therefore, the ordinary ray
travels with the same speed in all the directions while extraordinary ray has different speed in
different directions.
There are two types doubly refracting crystals: 1. Uniaxial and 2. Biaxial.
In uniaxial crystals there is only one direction along which the two refracted rays travel
with the same velocity (examples are calcite, tourmaline and quartz). In biaxial crystals, there are
two such directions along which the velocities are the same (examples are topaz, aragonite etc).
The phenomenon of double refraction can be illustrated with the following simple
experiment. An ink dot is made on a white paper, and a calcite crystal is placed over it. Now,
looking through the top face, two images are observed. If now the crystal is rotated slowly, one
image remains stationary while the other rotates in the direction of rotation of crystal. The
stationary image is known as ordinary image while the rotating image is known as extraordinary
image.
1.3.9 NICOL PRISM:
Principle:
When an unpolarized light is transmitted through a calcite crystal, it splits into two beams
namely o-ray and e-ray. These beams are completely plane polarized with vibrations perpendicular
to each other. If by some means one beam is eliminated then the emergent beam from calcite
crystal will be plane polarized light. This is achieved by using a Nicol prism.
Construction:

Consider a calcite crystal whose length is three times as that of its width. The end faces of
the crystal having an angle 71˚ and 109˚ with the principle section. The calcite crystal is cut into
two pieces along the plane (PS) perpendicular to the principle section and as well as the end faces

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PR and QS of the crystal. The end faces of the crystal are grounded in such a way that the angle in
the principle section becomes 68˚ and 112˚ instead of 71˚ and 109˚. This is done to increase the
field of view. The two cut pieces are cemented together by Canada balsam. Canada balsam is a
transparent substance and it is optically more dense e-ray and less dense than o-ray. That means
the refractive index Canada balsam is lies between the refractive indices of o-ray and e-ray. For
sodium light μ0 = 1.6584, μCB = 1.55 and μe = 1.4864.
Working:
When a beam of unpolarized light enters into Nicol prism, it is doubly refracted into
ordinary plane polarized light and extra ordinary plane polarized light. From the values of
refractive indices, it is clear that Canada balsam acts as a rarer medium for an o-ray and denser
medium for an e-ray. Therefore, there exists a critical angle of refraction for the o-ray at the
interface of calcite crystal and Canada balsam surfaces but not for the e-ray. Under these
conditions, if angle of incidence of the o-ray at Canada balsam greater than critical angle 69˚, it
gets total internal reflection. The extra-ordinary ray is not totally reflected because it is traveling
from a rarer to denser medium. Thus, only extra-ordinary ray is transmitted. Since e-ray is plane
polarized having vibrations parallel to principle plane, the light emerging from the Nicol’s prism
is plane polarized.
Uses:
Two Nicol’s prisms lined up one behind the other are often used in optical microscopes for
studying optical properties of the crystal. The first Nicol, which is used to produce the plane
polarized light, is called the polarizer and the second Nicol, which is used to test the light, is called
the analyzer.

1.3.10. QUARTER WAVE AND HALF WAVE PLATES

When a plane polarized light of wavelength λ is incident normally on a thin plate of uniaxial
crystal cut parallel to its optic axis, the light splits up into ordinary and extraordinary plane
polarized lights. They propagates along the same direction but different velocities. In positive
crystals like quartz, the o-ray travels faster than e-ray. The e-ray is travels faster than o-ray in
negative crystals like calcite, because the refractive index of e-ray is less compared to that of o-
ray. As a result phase difference as well as path difference is introduced between them when they
emerged out from other face. Hence the path difference between the two rays is
Δ = (μe ~ μo)t
Two types of obstruction plates are used in optical instruments.

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1. Quarter wave Plate

2. Half wave Plate
1.3.10.1. Quarter wave plate:
If the thickness of the crystal is such that it introduces a phase
difference of /2 or a path difference of /4, then the light
emerging from this crystal is circularly polarized. Such a
crystal is called Quarter wave plate.
λ
∆ = (µo~ µe) t =
4
λ
Thickness of Quarter wave plate, t 
4( µo ~ µe )
Where o and e are refractive indices of the crystal for
ordinary and extra ordinary waves.

Uses of quarter wave plate

If linearly polarized light is incident on a quarter-wave plate at 45° to the optic axis, then
the light is divided into two equal electric field components. One of these is retarded by a quarter
wavelength. This produces circularly polarized light.
If circularly polarized light is incident on quarter wave plate at 45° to the optic axis then it
produces linearly polarized light.
If linearly polarized light is incident on quarter wave plate other than 45° to the optic axis
then it produces elliptical polarized light.

1.3.10.2. Half wave plate:

If the thickness of the crystal is such that it introduces a phase difference of or a path
difference of /2, then the light emerging from this crystal is circularly polarized. Such a crystal is
called Half wave plate.
λ
∆ = (µo~ µe) t =
2
λ
Thickness of Quarter wave plate, t 
2( µo ~ µe )
Where o and e are refractive indices of the crystal for ordinary and extra ordinary waves.
Note: When the phase difference is 0, , 2, 3, 4, ... or path difference is 0, λ/2, 2λ/2, 3λ/2, ….
the resultant light is a linearly polarized light.

Use of half wave plate

Half wave retarders can rotate the polarization of linearly polarized light to twice the angle
between the optic axis and the plane of polarization. Placing the optic axis of a half wave retarder
at 45° to the polarization plane results in a polarization rotation of 90° to its original plane.

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1.3.11 PRODUCTION OF CIRCULARLY AND ELLIPTICALLY POLARISED LIGHT

(1) Circularly Polarized Light

Circularly polarized light is the resultant of two waves of equal amplitudes, vibrating at
right angles to each other and having a phase difference of π/2. Following (Fig. 3.16) is the
experimental arrangement to obtain circularly polarized light.

A beam of monochromatic light is allowed to fall on a Nicol prism N1. The emergent light
from Nicol N1 is plane polarized light. Another Nicol prism N2 is placed at a certain distance in a
crossed position, i.e., no light transmits from it. The field of view will be dark when observed from
the eye in this position.
Now, a quarter wave plate Q mounted on a tube T1 which is introduced between the two
Nicols and hold normal to the incident beam. The tube T1 can rotate about the outer fixed tube T2.
Thus, the λ/4 plate can be rotated about a horizontal axis through any desired angle. By the
introduction of λ/4 plate between N1 and N2 the field of view after N2 is not dark, i.e., there is some
light.
The quarter wave plate is now rotated till the field of view is again dark. This happens
when vibrations of light incident on quarter wave plate are along the optic axis and so
perpendicular to N2. Now, the quarter wave plate is rotated through 45° so that the vibrations of
light incident on it makes angle 45° with its optic axis. At this position the amplitude of ordinary
and extraordinary wave becomes equal.
According to the property of λ/4 plate a phase difference of π/2 is introduced between
ordinary and extraordinary rays so that resultant beam after quarter-wave plate will be circularly
polarised light.
(2) Elliptically polarised light
Elliptically polarised light is the resultant of two waves of unequal amplitudes vibrating at
right angles to each other and having a phase difference of π/2. To obtain the elliptically polarised
light, the experimental arrangement is the same as shown in fig. 3.16. A parallel beam of
monochromatic light is allowed to fall on two Nicols in crossed position. In this case the field of
view is dark. A λ/4 plate is now introduced between the two Nicols so that the field of view may
be bright. The quarter wave plate is rotated in such a way that the field of view is again dark. Again
the quarter wave plate is rotated such that vibration of light incident on it makes any angle other
than 45°. This makes the amplitudes of ordinary and extraordinary rays unequal and so the
resulting light from quater-wave plate is elliptically polarised.

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1.3.12 CONVERSION OF ELLIPTICALLY POLARISED LIGHT INTO CIRCULARLY

POLARISED LIGHT
We know that elliptically polarised light is made up of two polarised lights of unequal
amplitudes at right angles to each other and having a phase difference of π/2. When a quarter-wave
plate is placed in the path of this light such that its optic axis is parallel to either the major or minor
axis of elliptically polarised. So further phase difference of π/2 is introduced.
Hence, the light emerging from quarter-wave plate becomes plane polarised light. In this
way, the elliptically polarised light first of all is converted into plane polarised light. Again this
plane polarised light is allowed to fall on a quarter-wave plate such that the plane of vibration of
plane polarised light makes an angle 45° with the optic axis. The quarter-wave plate breaks the
incident light (plane polarised light) into ordinary and extraordinary waves of amplitude and
introduces a phase change of π/2. Thus, the emergent light is circularly polarised light.

1.3.13 DETECTION OF PLANE, CIRCULARLY AND ELLIPTICALLY POLARISED

LIGHT
i) Plane Polarised Light
The light beam is allowed to fall on Nicol prism. If on rotation of Nicol prism, intensity of emitted
light can be completely extinguished at two places in each rotation, then light is plane polarised.
ii) Circularly Polarised Light
The light beam is allowed to fall on a Nicol prism. If on rotation of Nicol prism the intensity
of emitted light remains same, then light is either circularly polarised or unpolarised.
To differentiate between unpolarised and circularly polarised light, the light is first passed through
quarter wave plate and then through Nicol prism. Because if beam is circularly polarised then after
passing through quarter wave-plate an extra difference of λ/ 4 is introduced between ordinary and
extraordinary component and gets converted into plane polarised.
Thus on rotating the Nicol, the light can.be extinguished at two plates.
If, on the other hand, the beam is unpolarised, it remains unpolarised after passing through
quarter wave plate and on rotating the Nicol, there is no change in intensity of emitted light.
iii) Elliptically Polarised Light.
The light beam is allowed to fall on Nicol prism. If on rotation of Nicol prism the intensity
of emitted light varies from maximum to minimum, then light is either elliptically polarised or a
mixture of plane polarized and unpolarised.
To differentiate between the two, the light is first passed through quarter wave plate and
then through Nicol prism. Because, if beam is elliptically polarised, then after passing through
quarter wave plate, an extra path difference of λ/ 4 is introduced between 0-ray and E-ray and get
converted into plane polarized. Thus, on rotating the Nicol, the light can be extinguished at two
places.
On the other hand, if beam is mixture of polarised and unpolarised it remains mixture after
passing through quarter wave plate and on rotating the Nicol intensity of emitted light varies from
maximum to minimum.

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1.3.14 OPTICAL ACTIVITY

The ability of substance (crystal or solution) to rotate plane of polarisation about the
direction of light is called as optical activity. The substance (crystal or solution) which can rotate
plane polarised light is called as optical active substance.

Working:
Two Nicols are set in a crossed position. The field of view is dark. Now, a quartz plate cut
with its faces parallel to the optic axis is introduced in between two Nicols, the field of view is not
dark. But by slightly rotating the Second Nicol N2 (i.e., for some different position of N1), the field
of a view is again dark. This suggests that the light emerging from quartz is still plane polarised
but the plane of polarisation has rotated through certain angle. This property of rotating the plane
of vibration of plane polarised light about its direction of travel by some crystal is known as optical
activity.

There are two types of optically active substance

1) Dextro rotatory
The substance which rotates the plane of vibration in the clockwise with respect to the
observer looking towards the source from the analyser is called as Dextro rotatory (right handed).
Ex., Fruit Sugar, quartz crystal, etc.
2) Laevo Rotatory
The substance which rotates the plane of vibration in the anticlockwise with respect to the
observer looking towards the source from the analyser is called as Laevo rotatory (left handed).
Ex. Cane sugar solution
The amount of the angle of rotation depends on the phase difference between two circularly
polarised beams in optical active substance.
Biot observed the following facts about the optical rotation:
(i) The amount of rotation θ produced by an optically active substance is proportional to its
thickness (l) traversed, i.e., θ ∝ l.

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(ii) In case of solutions and vapours, the amount of rotation for a given path length is proportional
to the concentration (C) of the solution or vapour, i.e., θ ∝ C
(iii) The rotation varies inversely as the square of wavelength (λ) of light employed, i.e., θ ∝ 1/λ.
Thus, it is least for red and greatest for violet.
(iv) The total rotation (θ) produced by a number of optically active substances is the algebraic sum
of the rotations (θ1, θ2, θ3, etc.) produced by individual specimens, i.e.,
θ = θ1+ θ2+ θ3+…
(the rotation in the anti-clockwise direction being taken as positive and that in the clockwise
direction as negative).
1.3.15 SPECIFIC ROTATION:
“The specific rotation of a substance at a particular temperature and for a given wavelength
of light used may be defined as the rotation produces by one decimeter length of its solution when
the concentration is 1 gm/cc.
θ
Thus specific rotation S =
lC
Where l is measured in decimeters
θ is measured in degrees
C is measured in gm/cc.
10
Note: S  , where l is measured in cm.
lC
Here, the angle of rotation in degrees

1. is directly proportional to the length of the solution in decimeter (l ) and

2. is directly proportional to concentration (c) of solution in gm/cc.
i.e., θ α l
αC
θαlC
θ = Sl C
Where ‘S’ is called specific rotation.
1.3.16 LAURENT’S HALF SHADE POLARIMETER:-
The instrument used for determination of angle of rotation of an optically active substance is
called a polarimeter. When it is used for finding the concentration of sugar solution it is called
saccharimeter.

Department of BS-Physics Division, VISHNU INSTITUTE OF TECHNOLOGY, BHIMAVARAM [14]

B.TECH I SEMESTER ENGINEERING PHYSICS-UNIT I

Construction:
The essential parts of a Laurent's half-shade polarimeter are shown in fig. 3.20. The polarimeter
consists of a source of light S, a convex lens L, a polariser P a half shade device, glass tube,
analyser and telescope. Here hollow glass tube having a large diameter in the middle is used so
that no air bubble may be in the path of light when filled with a liquid. A parallel beam of light
obtained from a source S of a monochromatic light is made to fall on a polariser P, the emergent
light will be plane polarised. This plane polarised light passes through a half shade device and then
through the tube containing the solution of optically active substance. The emergent light passes
through analyser which is viewed through a telescope.
Action of half-shade
When an optical active substance is placed in between two crossed Nicols the field of view
is not dark. In order to make the field of view dark, the analyser is rotated. It is observed that when
the analyser is rotated the field of view is not dark, for a considerable region. Hence, the
measurement of optical rotation is not accurate.

To avoid this difficulty a half shade device is used. The Laurent's half-shade plate consists
of a semi-circular half-wave plate ABC of quartz (cut parallel to optic axis) so that it introduces a
phase angle of π between extraordinary and ordinary rays. A semi-circular glass plate ADC is
cemented along the diameter AC. The thickness of the glass plate is such that it absorbs the same
amount of light as the quartz plate. Let the plane of vibration of the plane polarised light incident
normally on half-shade plate be along PO. Here, PQ makes an angle θ with AC. The vibrations
emerge from the glass plate as such, i.e, along the plane PQ. Inside the quartz plate, the light is
divided into two components one ordinary component along XX and the other extraordinary
component parallel to optic axis, i.e., along YY axis. The two components travel along the same
direction but with different speeds. The ordinary component moves with greater velocity than
extraordinary component and on emergence a phase difference of t is introduced between them.
Due to this phase difference the direction of ordinary component is reversed, i.e., if the
initial position of ordinary component is represented by OM [fig. 3.21], then the final position
should be represented by ON. Now, the resultant of extraordinary component OL and ordinary
component ON will be OR making angle θ with Y-axis. Thus, the vibration of the beam emerging
out of quartz will be along RS.
If the principal plane of the analysing Nicol is parallel to PQ, then the light from glass
portion will pass unobstructed while light from quartz will be partly obstructed. Due to this fact
the glass half will appear brighter than the quartz half.

Department of BS-Physics Division, VISHNU INSTITUTE OF TECHNOLOGY, BHIMAVARAM [15]

B.TECH I SEMESTER ENGINEERING PHYSICS-UNIT I

On the other hand, if the principal plane of the analyser is parallel to RS, the light from
quartz portion will pass unobstructed while light from glass will be partly obstructed. Thus, the
quartz half will appear brighter than the glass half If, however, the principal plane of analyser is
parallel to AC (Y-axis), it is equally inclined to the two plane polarised lights and hence the field
of view will be equally bright. Thus, the half shade serves the purpose of dividing the field of view
in two halves. When the analysing Nicol is slightly rotated from the position of equal brightness a
marked change in the intensity of two halves is observed.
Procedure:
First the tube is filled with distilled water and replace at its position. Looking through the
telescope the analyser is rotated till the field of view is equally bright. The reading on the circular
scale is noted as θ1.
Now the tube is filled with given solution and replace it in this position. On looking through
the telescope we find that one half of the field of view is less bright than the other. Then again the
analyser is rotated till the field of view becomes equally bright. The reading on the circular scale
is noted as θ2.The difference of two readings gives an angle θ. Here θ is called as the angle of
rotation.
θ = θ1~θ2
The length of the solution in the tube is measured, by knowing the value of C. we can
calculate the specific rotatory power by using the formula.
10
S
lC
Where l = length of solution in cm.
C = concentration of the solution in gm/cc.

Department of BS-Physics Division, VISHNU INSTITUTE OF TECHNOLOGY, BHIMAVARAM [16]