Polarization of Light by Mr. Charis

Mr. A.CHARIS ISRAEL. M.Sc., B.Ed., (Ph.D.)

Sr. Lecturer of PHYSICS

Mobile No: +91-9269680853

PHYSICS-I UNIT –II POLARISATION OF LIGHT 2009-2010

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PHYSICS – I for R T U

UNIT – II

POLARIZATION

Unpolarized Light: Light which consists of an infinite number of waves,

each having its own direction of vibration is called unpolarized light.

Polarized Light: Light which acquired only one direction of vibration is

called polarized light.

(or)

Light which has acquired the property of one-sidedness is called

polarized light.

Plane Polarized Light: When the vibrations are confined to a single direction at right angles

to the direction of propagation, then light is called plane polarized light.

Plane of vibration, plane of polarization and direction of propagation:

Plane of Vibration: The “plane in which the vibrations of

the polarized light are confined” is called plane of

vibration.

The plane of vibration contains the “direction of

propagation of wave” and “direction of vibration”.

Plane of Polarization: The “plane passing through the direction of

propagation and perpendicular to the plane of vibration” is

known as plane of polarization.

(or)

The “plane which has no vibrations of wave” is

called plane of polarization.

PLANE, CIRCULAR AND ELLIPTICALLY POLARISED

LIGHT ON THE BASIS OF ELECTRIC VECTOR:

Light waves are “Electromagnetic waves”.

Electromagnetic wave: A transverse wave consisting of electric and

magnetic fields vibrating perpendicular to each other and

perpendicular to the direction of propagation is an electromagnetic

wave.

The vibrating electric vector ‘E’ and the direction of wave

propagation constitute a plane called “plane of vibration”.

The magnetic vector ‘H’ and the direction of propagation of wave

form a plane, called “plane of polarization”.

It is electric vector which is most effective in a light wave, so we always refer the light wave with electric

vector E, it is always perpendicular to the direction of propagation of the wave.

(i) Plane polarized Light: During the propagation of

light, if the electric vector E vibrates parallel and

confined to a single plane perpendicular to the direction

of propagation, then the wave is said to be plane

polarized light.

If wave is propagating along Z-axis, then the

electric vector E appears linearly, if observed along Z-direction back towards origin as shown in figure. Therefore, the

plane polarized light is also called as “linearly polarized light”.

U n p o l a r i s e d L i g h t

P o l a r i s e d L i g h t w i t h

v i b r a t i o n s p a r a l l e l t o

th e p la n e o f p a p e r

P o l a r i s e d L i g h t w i t h v i b r a t i o n s p e r p e n d i c u l a r

t o t h e p l a n e o f p a p e r

plane of vibration

direction of propagation

direction of propagation

plane of vibration

plane of polarisation

direction ofpropagation

plane of polarisation

plane of

vibration

E lectric

,Magnetic Vector M

Vector

E

B xE

yE x yE iE jE= +

θ

E

E

0xE =

yE

O

X

Y

Z

0x y

E or E =0∅=

X

Y

X

Y




If electric vector is oriented at an angle ' 'θ to the X-direction as shown in figure, then x yE and E are the

components of ‘E’ along X and Y-axes respectively. Thus, x yE iE jE= + .

Therefore, a plane polarized light is a wave whose angle ' 'θ remains constant in time or 0∅ = and one of the

components of Electric vector ( )( ) 0x yE or E = is always zero.

(ii) Circularly Polarized Light: Suppose that the components x yE and E and are equal in magnitude ( )x yE E= but

differ in phase by ' 2 'π i.e., 2π∅ = .

When such components superpose, the

magnitude of the resultant vector E

remains constant but rotates about the

direction of propagation such that it goes

on sweeping a circular helix in space as

shown in figure. Thus such a wave is

called Circularly polarized light.

In circular polarization, the electric vector E completes one revolution in space in a distance of one wave length.

If the point of observation is along the Z-axis, then the tip of Electric vector E traces a circle with the direction of

propagation as a center. If the rotation of the tip of electric vector is clockwise, then the light is said to be

Right-Circularly polarized light. If the rotation of the tip of electric vector is anti-clockwise, then the light is said to be

Left-Circularly polarized light.

(iii) Elliptically Polarized Light:

Suppose that the components and are not equal i.e., ( )x yE E≠ and also they differ in phase i.e., 0∅ ≠ . When

these two waves superpose, the magnitude

of their resultant vector E changes with

time and the vector E also rotates about

the direction of propagation. The tip of the

vector E sweeps a flattened helix in space

as shown in figure. Such a wave is called

Elliptically Polarized Light.

If the rotation of the tip of the

electric vector is clockwise, then the light is said to be Right-Elliptically polarized light. If the rotation of the tip of the

electric vector is anti-clockwise, then the light is said to be Left-Elliptically polarized light.

MALUS LAW:

Malus discovered a law regarding the Intensity of light transmitted by the analyzer.

Statement: When a completely plane polarized light beam is incident on the analyzer, the intensity of the polarized

light transmitted through the analyzer changes as the square of the cosine of the angle between the plane of

transmission of the analyzer and plane of transmission of the polarizer.

This law fails when the light is not completely plane polarized.

Proof: Let OP = a, be the amplitude of the incident plane polarized light from the

polarizer. OA be the plane of transmission of analyzer and θ be the angle between

the planes of transmission of polarizer and analyzer.

Now, the amplitude of incident plane polarized light can be resolved in two

components, one parallel to the plane of transmission of the analyzer OA ( )cosa θ

and the other perpendicular to it along OB ( )sina θ .

Hence, the component ( )cosa θ is transmitted through the analyzer.

∴Intensity of light transmitted through the analyzer is ( )2 2 2

cos cos (1)I a aθ θ θ= = →

B

E

O

XY

Z

θ θ θ

E

X

Y

E

X

Y

O O

R igh t C ircu larly

po larised light

L eft C ircu larly

po larised light

C ircularly po larised light

m aking helica l pa th

( )x yE E=

yE

xE

yE

xE

2π∅=

B

E

O

XY

Z

θ θ θ

E

X

Y

E

X

Y

O O

R igh t E llip tica lly

po larised ligh t

L eft E llip tically

po larised ligh t

E llip tica lly polarised ligh t

m aking flattened helica l path

( )x yE E≠

yE

xE

yE

xE

0∅≠

cosa θsina θ

O

AB

P

P la n e o fP o la r izer

A n a lyzer P la n e o f

a

θ




If ‘I’ be the intensity of the incident polarized light, then 2 (2)I a= →

2 2 cos (or) cos (3)I I Iθ θθ θ∴ = ∝ →

Hence, the intensity of light transmitted through an analyzer inclined at an angle θ with the plane of

transmission of polarizer is proportional to the square of cosine of the angle θ .

Case (i): When planes of transmission of polarizer and analyzer are parallel . ., 0,i e θ =

Then I Iθ = i.e., the total intensity of light transmitted through polarizer is transmitted through the analyzer.

Case (ii): When planes of transmission of polarizer and analyzer are perpendicular . ., 90 ,oi e θ =

Then 0Iθ = i.e., no light is transmitted through analyzer.

DOUBLE REFRACTION:

Principle: When a light ray is incident on a transparent anisotropic crystal, it is divided into two refracted rays with

different velocities and in different directions. This phenomenon is called Double refraction.

Ex: Calcite, Quartz, mica etc exhibit double refraction.

Calcite Crystal: Calcite crystal is a colorless transparent crystal, chemically called as

Hydrated Calcium Carbonate (CaCO3). The structure of a Calcite crystal belongs

to the hexagonal system, a rhombo-hedral. The six faces of a rhombo-hedron are

parallelograms each having angles of 101 55 'o

and 78 5 'o

as shown in figure.

There are two opposite corners A and B where the three obtuse angles (101 55 ')o

meet together. These corners are known as Blunt Corners. Calcite is a Uni-axial

Negative Crystal.

Optic Axis: A line passing through the blunt corners and making equal angles with three faces which meet at this blunt

corner, locate the direction of the Optic axis.

(i) A ray of light propagating along the optic axis does not suffer double refraction.

(ii) Optic ray divides the crystal into two symmetrical parts. So, optic axis is the axis of symmetry of a crystal.

(iii) Any line in the crystal which is parallel to optic axis is also an optic axis.

Principal Section: Any plane in a crystal, which contains optic axis and is perpendicular to two opposite faces is called

a principal section.

Ordinary ray (or) o-ray: The refracted ray, which always obeys the ordinary laws of refraction (Snell’s law) and

having vibrations perpendicular to the principal section is known as o-ray.

(i) The o-ray travels with the constant velocity in all directions in the crystal.

(ii) The refractive index ' 'oµ of o-ray is also constant, throughout the crystal.

(iii) An o-ray is a plane polarized light.

(iv) Along Optic axis an o-ray has constant velocity.

Extra-ordinary ray (or) e-ray: A refracted ray which does not obey the laws of refraction (i.e., does not obey snell’s

law) and having vibrations parallel to the principal section is called as e-ray.

(i) The e-ray has different velocities in different directions of the crystal.

(ii) The refractive index of e-ray varies with direction of incidence ray.

(iii) An e-ray is also a plane polarized light.

(iv) Along the Optic axis of a crystal, an e-ray travels with constant velocity.

Principal Section of o-ray: The plane of a crystal containing optic axis and o-ray is called Principal section of o-ray.

Principal section of e-ray: The plane of a crystal containing optic axis and e-ray is called Principal section of e-ray.

Uni-axial crystals: A crystal which contains only one direction along which the two refracted rays (o-ray and e-ray)

travel with the same velocity is called Uni-axial crystal.

(or) A crystal with one optic axis is called Uni-axial crystal.

A

B101 55 'o

101 55 'o101 55 'o

78 5 'o

C alcite

Blunt C orners

OpticAxis




Ex: Calcite, Quartz, Tourmaline, etc.

Bi-axial Crystal: A crystal which contains two directions along which the two refracted rays (o-ray & e-ray) travel

with the same velocity is called Bi-axial crystal.

(or) A crystal with two optic axes is called Bi-axial crystal.

Ex: Mica, Topaz, Aragonite etc.

Negative crystals: A crystal in which the refractive index ' 'oµ of ordinary ray is greater than the refractive index ' 'eµ

of e-ray is called Negative crystal i.e., o eµ µ> .

In Negative crystals e-ray travels faster than the o-ray i.e., ve > vo .

Ex: Calcite.

Positive Crystals: A crystal in which the refractive index ' 'eµ of e-ray is greater than the refractive index ' 'oµ

of o-ray

is called a positive crystal i.e., e oµ µ> .

In positive crystals ordinary ray moves faster than extra-ordinary ray i.e., vo > ve .

Ex: Quartz, ice, etc.

Bifringence ' 'µ∆ : Bifringence of a crystal is defined as, e oµ µ µ∆ = − .

If e oµ µ> , ' 'µ∆

is a positive quantity, so for positive crystals, Bifringence is positive.

If o eµ µ> , ' 'µ∆

is a negative quantity, so for negative crystals, Bifringence is negative.

Refracted rays (o-ray & e-ray) in Calcite: A Calcite crystal comes under the category of Uni-

axial Negative crystals.

When a light ray AB is incident on a Calcite crystal at

an angle of incidence ‘i’ with the normal N as shown in

figure, the ray breaks up (refracts) into ordinary and extra-

ordinary rays.

The ordinary ray travelling along BD makes an angle

of refractionor∠ and extra-ordinary ray travelling along BC makes an angle of refraction

er∠ with the normal N.

In Calcite o er r∠ < ∠ , so, refractive index of o-ray and e-ray are given as,

sin sin

sin sino e

o e

i iand

r rµ µ= = .

QIn Calcite o er r∠ < ∠ , so,

o eµ µ> . Hence velocity of o-ray is less than the velocity of e-ray i.e., vo < ve.

So, in Calcite crystal the relation between refracting angles, refractive indices and velocities of o-ray and e-ray

are as follows:

o er r∠ < ∠ ,

o eµ µ> and vo < ve .

NICOL PRISM:

Nicol prism is a device for producing and analyzing a plane polarized light.

Principle: The ordinary ray (o-ray) produced in the Calcite crystal is eliminated by the Total Internal Reflection (TIR)

from the crystal by splitting the crystal into two pieces and then pasted with a thin film of Canada Balsam. So, only

e-ray which is completely plane polarized light transmits the

Nicol prism.

Construction: A Calcite crystal whose length is three times it

width is taken and the end faces are grounded so that principal

section will have 68o and 112

o, to increase the field of view.

Now, the principal section is cut into two pieces along

PR and QS, polished and then cemented together by Canada

Balsam.

The refractive index ( )Cµ of Canada Balsam is related as, e C oµ µ µ< < .

For sodium D lines, 1.658, 1.55 1.486o c eandµ µ µ= = =

i∠

A

BN

'N

90o

90o

S

P Q

R o ray−

e ray−

O

Canada Balsam

109o

71oA

Bi∠

or∠ er∠

C

D o ray−

e ray−N




Working: When an unpolarised light AB is incident on the face PR of the prism, it is doubly refracted into ordinary ray

and extra-ordinary ray.

From the values of refractive indices of Canada balsam, o-ray and e-ray, Canada balsam acts as a rarer medium

for o-ray and as a denser medium for e-ray. Also, the dimensions of the crystal are chosen such that the angle of

incidence of o-ray is greater than the critical angle. Under these conditions, the o-ray can be eliminated from the prism

by Total Internal Reflection at the surface of the Canada balsam.

But e-ray is moving from rarer to denser medium so does not obey TIR and is transmitted through the Canada

balsam and emerges out of QS of Nichol prism. Because e-ray is a plane polarized light, having vibrations parallel to

the principal plane, the light emerging from the Nichol prism is plane polarized.

Limitations: Nichol’s prism can be used as both polarizer and analyzer.

HUYGEN’S THEORY OF DOUBLE REFRACTION:

According to Huygen’s theory, each point on a wavefront acts as a fresh source of wave and generates

secondary wavelets. This theory as such could not explain the phenomenon of double refraction. So, Huygen extended

his theory of secondary wavelets to explain double refraction in uni-axial crystals.

According to this theory,

(i) When any wavefront strikes a double refracting crystal, every

point of the crystal becomes a source of two wavefronts.

(a) Ordinary wavefront, since o-ray has constant velocity in all

directions, the o-wavefront is spherical.

(b) Extra-ordinary wavefront, since e-ray has different

velocities in different directions, the e-wavefront is ellipsoid,

with optic axis as the axis of revolution.

(ii) The sphere and ellipsoid touch each other along the optic axis of

the crystal, because the velocities of both o-ray and e-ray are

equal along optic axis.

(iii) In negative crystals, ellipsoid lies outside the sphere as shown in

figure, because in negative crystals e-ray moves faster than o-

ray.

(iv) In positive crystals, sphere lies outside the ellipsoid as shown in figure, because in positive crystals o-ray

moves faster than e-ray.

Theory: Consider a beam of plane polarized light obtained from Nicol prism falls normally on a Calcite crystal cut with

its optic axis parallel to its faces

as shown in figure.

Let ‘A’ be the maximum

amplitude of incident light which

makes angle θ with optic axis.

The plane polarized light on

entering the crystal is split up into

two components o-ray and e-ray,

with amplitude components ( )sinA θ along o-ray i.e.,

PO and ( )cosA θ along e-ray i.e., PE.

According to Huygen’s theory of double

refraction the o-ray and e-ray move with different

velocities and in same direction. After the rays transmit

the Calcite crystal, they have a phase difference δ

depending upon the thickness ‘t’ of crystal.

Optic Axis e wavefront−o wavefront−

in Calcite

in Quartz

i∠

A

BN

'N

90o

90o

S

P Q

R o ray−

e ray−

O

Canada Balsam

U npolarisedL ight

polarisedL ight

Calcite Crystal Nichol

cosA θ

sinA θ

A

E

O

P




The equations for such waves can be written as cos sin( ) (1)x A t for e rayθ ω δ= + − →

sin sin o (2)y A t for rayθ ω= − →

Let

sin( ) (3)x a tω δ= + →

sin (4)y b tω= →

From eqn.(4) sin (5)y

tb

ω = →

2

2cos 1 (6)

yt

bω

∴ = − →

Expanding eqn.(3) by using eqn’s (5)&(6), we have

(sin cos cos sin )x a t tω δ ω δ= + ⇒

2

2cos 1 sin

x y y

a b bδ δ

= + −

⇒

2

2cos 1 sin

x y y

a b bδ δ

− = −

by squaring and expanding the above eqn, we have

⇒

2 2 22 2 2

2 2 2

2 coscos sin sin

x y xy y

a b ab b

δδ δ δ+ − = −

2 22 2 2

2 2

2 cos (sin cos ) sin

x y xy

a b ab

δδ δ δ⇒ − + − =

2 22

2 2

2 cos sin (7)

x y xy

a b ab

δδ⇒ + − = →

The above eqn.(7) is the General equation of Ellipse.

Case (1): When 0, sin 0 cos 1andδ δ δ= = =

∴from eqn.(7), 22 2

2 2

2 0 0 0 (8)

x y xy x y x y by x

a b ab a b a b a

+ − = ⇒ − = ⇒ − = ⇒ = →

This is the equation of straight line. Therefore the light will be plane polarized light with vibrations in the same plane

as in incident light.

Case (2): When (2 1) , 0,1,2,.... . ., ,3 ,5 ,........2 2 2 2

n n i eπ π π π

δ δ= + = =

sin 1 cos 0then andδ δ= =

Then eqn.(7) reduces to

2 2

2 2 1 (9)

x y

a b⇒ + = →

This represents the equation of a symmetrical ellipse. Thus the emergent light in this case will be Elliptically polarized

light.

Case (3): When , 2

and a b thenπ

δ = =

Eqn.(7) becomes

2 2 2 (10)x y a⇒ + = →

This represents a circle. Thus the emergent light will be Circularly polarized light.

cos sin , A a and A b thenθ θ= =

0δ =

a

b

32

πδ =

a

b2

πδ =

a

b

2

πδ =

a

a




PHASE RETARDATION PLATES:

Phase retardation plates are used to change the state of polarization of an incident light.

Working: When plane polarized light is incident on a phase retardation plate, it splits the light into o-ray and e-ray,

which are plane polarized, vibrating perpendicular to one another and one wave lags behind the other by a known

quantity. Now, when these two waves emerge out of crystal and superimpose, then the resultant wave is of a different

state of polarization.

Ex: Quarter-wave plate and Half-wave plate are the important phase retardation plates.

Quarter-wave plate (QWP):

A crystal plate which introduces a phase difference of 2

π radians or a path difference of 4

λ between o-ray

and e-ray is called a Quarter-wave plate (QWP).

Construction of QWP: A Calcite plate is cut with optic axis parallel to the surface. The thickness ‘t’ of such a plate can be calculated as

below.

If oµ and eµ be the refractive indices of the crystal for o-ray and e-ray, then the

optical path difference between o-ray and e-ray is,

( ) ( )o e o e o et t t in Calciteµ µ µ µ µ µ∆ = − = − >Q

But a Quarter-wave plate introduces a path difference of 4

λ∆ =

4o et t λµ µ∴ − =

( )4 o e

tλ

µ µ=

−

∴ If the thickness of a uni-axial Calcite crystal is ( )4 o e

λµ µ−

, then the plate introduces a phase difference of 2

πor a

path difference of 4λ

between o-ray and e-ray.

For positive crystals e oµ µ> , so,

( )4 e o

tλ

µ µ=

−.

Since a Quarter-wave plate introduces a phase difference of 90o, it is used to produce circular and elliptically

polarized light.

Half-Wave Plate (HWP):

A uni-axial crystal plate which introduces a phase difference of ' 'π or a path difference of 2

λ between o-ray

and e-ray, then it is called a Half-Wave Plate.

Construction of HWP: A Calcite plate is cut with optic axis parallel to the surface. The thickness ‘t’ of such a plate can be calculated as

below.

If oµ and eµ are the refractive indices of o-ray and e-ray, then the path difference between o-ray and e-ray is given by,

( ) ( )o e o e o et t t in Calciteµ µ µ µ µ µ∆ = − = − >Q

But a half-wave plate introduces a path difference of 2

λ∆ =

2o e

t t λµ µ∴ − =

( )( )

2 o e

t for uni axial crystalsλ

µ µ= −

−

For positive crystals, ( )

( ) 2

e o

e o

t in positive crystalsλ

µ µµ µ

= >−

Q

t

Optic Axis




PRODUCTION OF CIRCULARLY AND ELLIPTICALLY POLARIZED LIGHT ( USING QWP ):

Production of Elliptically polarized light using QWP: Let a ray of plane polarized light be incident on a Quarter-wave plate such that the electric vector ‘E’ makes an

angle θ with the optic axis. Now the ray is divided into o-ray and e-ray of different amplitudes E2 and E1 which are

equal to ( )sinE θ and ( )cosE θ respectively. The rays move along the same path but with different velocities. The ray

having its vibrations parallel to the optic axis is e-ray and the other having vibrations normal to the optic axis is o-ray.

The two waves are coherent and start in phase at the front face of the quarter-wave plate, but progressively get

out of phase as they propagate through the crystal. When the two rays reach the rear face and emerge out of the crystal

plane, they will have a phase difference of 2π .

If 2, cos 0 sin 1then andδ π δ δ= = =

Then according to the equation, 2 2

2

1 2 1 2

2cos sin

y x yxE E EE

E E E Eδ δ

+ − =

We have

2 2

1 2

1yx

EE

E E

+ =

The above equation represents an Ellipse. Therefore the resultant of the rays (o-ray & e-ray) is Elliptically

polarized light.

Production of Circularly polarized light using QWP: Let the plane polarized light be incident on the quarter-wave plate such that the electric vector ‘E’ makes an

angle 45oθ = with the optic axis.

Now, 1 cos cos 45

2

o EE E Eθ= = =

and

2 sin sin 452

o EE E Eθ= = =

1 2 0. ., 2

Ei e E E E= = =

Now, the two rays are coherent and start in phase at the point of entry and emerge out at the rear face of the

crystal with a phase difference 2.δ π=

Substituting 1 2 0

2E E E and

πδ= = =

in the following equation

2 2

2

1 2 1 2

2cos sin

y x yxE E EE

E E E Eδ δ

+ − =

Then we have

2 2

0 0

1yx

EE

E E

+ =

2 2 2

0 x yE E E⇒ + =

The above equation represents a circle. Therefore, the resultant ray coming out of QWP is a Circularly

polarized light.

Thus, we can produce circularly or elliptically polarized light by using a quarter-wave plate depending upon the

angle of incident electric vector ‘E’ with the direction of the optic axis of the quarter –wave plate.

Action of the QWP on Elliptically and Circularly polarized light: Let us consider elliptically polarized light incident on a quarter-wave plate. Elliptically polarized light may be

viewed as made up of two coherent plane polarized waves of different amplitudes and differing in phase of 2.π The

quarter-wave plate introduces an additional phase difference of 90o leading to a total phase difference of ' 'π between

the waves at the rear face of QWP.

Consequently, both the component waves will vibrate in the same plane, which result in a plane polarized light.

Similarly, the action of a quarter-wave plate on circularly polarized light is to convert it into plane polarized light.

θ

Optic axis

PlanePolarized

lightQWP

Polarizedlight

Elliptically

45oθ =

Optic axis

PlanePolarized

lightQWP

Polarizedlight

Circularly




DETECTION OF PLANE, CIRCULARLY AND ELLIPTICALLY POLARIZED LIGHT:

( USING POLARISER AND QWP )

Light may exhibit any one of the three types of polarizations or may be unpolarized or partially polarized. The

polarization of the light can be detected by using a polarizer and a Quarter-wave plate.

The following steps are used in the detection of the type of polarization.

1) A polarizer is placed into the path of the light of

unknown type of polarization. On rotating the

polarizer through on full rotation, if the transmitted

light intensity is extinguished twice, then the

incident light is plane polarized.

2) If the intensity of the transmitted light varies

between a maximum value and a minimum value but

does not become extinguished in any position of the

polarizer, then the incident light is either partially

polarized or Elliptically polarized.

3) On rotation of the polarizer, if the intensity of the

transmitted light remains with equal intensity in all

positions, then the incident light is either circularly

polarized or unpolarized.

To distinguish between the Elliptically polarized and partially polarized light or Circularly and

unpolarized light, we use a quarter-wave plate. Light is allowed to pass through Quarter-wave plate first and

then through the polarizer.

4) If the incident light is Elliptically polarized,

the quarter-wave plate converts it into a plane

polarized beam which on rotation of the polarizer be

extinguished twice.

On the other hand, if the transmitted

light varies between a maximum and a

minimum without becoming zero, then the

incident light is partially polarized.

5) If the incident light is circularly polarized,

the quarter-wave plate converts it into plane

polarized light on one complete rotation of the

polarizer, the light would be extinguished twice.

On the other hand, if the intensity of

the transmitted light remains constant on

rotation of the polarizer, then the incident

light is unpolarized light.

polarizer

Unknown

polarization 0

I

I

0Plane

Polarizedlight

polarizer

Unknown

polarization minI Partially

Polarized

lightmaxI

minI

maxI

Elliptically

Or

polarizer

Unknown

polarization

I

I

Circularly

Unpolarizedlight

I I Or

polarizer

0

I

I

0 Polarizedlight

QWP

PartiallyPolarized

light

Elliptically

Or Elliptically

polarizer

Polarizedlight

QWP

PartiallyPolarized

light

Elliptically

Or Partially

minI

maxI

minI

maxI

polarizer

0

I

I

0 Polarizedlight

QWP

Polarized

light

OrCircularly

Unpolarized

Circularly

polarizer

I

I

Polarizedlight

QWP

Polarized

light

OrCircularly

Unpolarized

Unpolarized

I I




OPTICAL ACTIVITY

Optically Active material: Materials having the ability of rotating the plane of polarization or the plane of vibration of a

plane polarized light on passing through them are called as Optically active materials.

Ex: Optically active Crystals: Quartz, Cinnabar, etc.

Optically active liquids: Turpentine, Tartaric acid, Nicotine, aqueous solution of sugar, etc.

Optical Activity: The property of a material, which rotates the plane of vibration or the plane of polarization of a plane

polarized light about an axis parallel to its direction, when allowed to pass through them is called optical activity. The

angle through which the plane of vibration is rotated is called as Angle of rotation.

LAW OF OPTICAL ROTATION:

According to this law,

“The amount of rotation θ of plane of polarization of a plane polarized light is directly proportional to

the concentration ' 'C of the liquid and the length ' 'l of the path of the light travelled through the solution”.

Mathematically it can be written as,

l and Cθ θ∝ ∝

l Cθ ∝

S l Cθ =

where ‘S’ is the constant of proportionality called as Specific rotation.

Some observed facts about Optical Rotation:

Biot observed the following facts about Optical rotation.

1) There are two types of optically active substances.

(i) The substances which rotate the plane of polarization in Clock-wise direction are called as

Dextro-rotatory or right handed substances.

(ii) The substances which rotate the plane of polarization in Anti-clock-wise direction are called as

Laevo-rotatory or left handed substances.

2) The rotation varies inversely as the square of the wavelength of the light used.

2

1θ

λ∝

Thus angle of rotation is least for Red and greatest for Violet.

3) The total rotation θ produced by a number of optically active substances is the algebraic sum of the rotations

1 2 3( , , ,......)θ θ θ produced by the individual specimens.

1 2 3 ( ......)θ θ θ θ∴ ∝ + + +

The rotation in the anti-clockwise direction is taken as positive and that in the clockwise direction as negative.

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 ' 'θ of plane of polarization of plane polarized light produced by one decimeter length ' 'l of the

solution when the concentration ' 'C is 1gm. per c.c.”

Thus, Specific Rotation, Sl C

θ=

×

where ' 'θ is the angle of rotation in degrees, ' 'l is the length of solution in decimeter and ' 'C is

the concentration of solution in gm. per c.c.




Measurement of Specific Rotation of a given liquid:

1) LAURENT’S HALF-SHADE POLARIMETER:

Polarimeter is an instrument used to determine the optical rotation of solution. It can also be used to find the

Specific rotation of sugar solution or if the specific rotation is known, then we can find its concentration.

Construction: The essential parts of a

Laurent’s polarimeter are as shown in

the figure. S is a monochromatic source

and L is a convex lens which makes the

incident rays into parallel beam. N1 and

N2 are two Nicol Prisms. N1 acts as a

Polarizer and N2 acts as an Analyzer. N2

is capable of rotating about an axis

through N1 and N2. The rotation of the analyzer can be read from the graduated circular scale C.S. The light after

passing through the N1 is allowed to pass through half-shade device (H.S.) and then through a glass tube T which holds

the optically active substance (here sugar solution). The glass tube T is a hallow tube having a large diameter in the

middle so that no air bubble may be in the path of the light when filled with liquid. It is also closed at the ends by over-

slips and metal covers. The ray after passing through the N2 is viewed by a telescope.

Half-shade device: The Laurent’s half-shade plate consists of a semi-circular half-wave plate ABC of quartz

(cut parallel to the optic axis) so that it introduces a phase change of ' 'π between e-ray and o-ray passing through it and

a semi-circular glass plate ADC as shown in the figure. These two plates are 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.

Action of Half-shade device: Let the plane of vibration of

the plane polarized light incident normally on half-shade plate is

along PQ. Here PQ makes an angle θ with AC. The light emerges

from glass plate along PQ whereas in quartz plate, the light is

divided into two components – one o-ray along XX’ and the other

e-ray along YY’. Now the o-ray moves faster than e-ray and on

emergence a phase difference of ' 'π is introduced between o-ray

and e-ray. Due to this phase difference the direction of o-ray is

reversed i.e., if the initial position of o-ray is OM then the final

position is ON. So, the resultant of e-ray along OL and o-ray along ON will be OR which makes an angle ' 'θ with the

Y-axis. Thus the vibration of the beam emerging out of quartz will be along RS.

If the principal plane of the analyzing Nicol is parallel to PQ, then light from glass plate will pass without

obstruction, and the light passing through quartz is obstructed. Due to this, the glass half will appear brighter than the

quartz half.

If the principal plane of analyzing Nicol is parallel to RS, the light from the quartz half will be pass without

obstruction, and the light passing through the glass half will be obstructed. Due to this, the Quartz half will appear

brighter than the glass half.

If the principal plane of analyzer is parallel to AC, it is equally inclined to the two plane polarized lights and

hence the field of view will be equally bright.

Determination of Specific Rotation: To determine the Specific rotation ‘S’ of a substance, a solution of known

concentration is prepared. The length of the solution is measured directly and the value of ' 'θ is determined as follows:

1) The glass tube is filled with water and placed in its proper position.

2) The telescope is focused on the half-shade and analyzer is rotated till equal bright position is obtained and

the reading of the vernier on the circular scale is noted as 1' 'θ .

3) Now the glass tube is filled with the optically active solution whose concentration is known and placed in its

proper position. The field of view in this stage will not be equally bright.

, Source S

1N Half shade−

( . .)device H S

' 'Glass Tube T2N

Polarizer Analyzer ' 'Convex lens L

S

Circular( . .)Scale C S

Telescope

. ' F ig L auren t s H alf shade P olarim eter−

monochromatic

Glass Quartz

PR

A

θ θ

D B

SQ

C

R

N'X O

'Y

Y

P

P X

L

θ θ




4) The analyzer is rotated and is brought to a position so that the field of view is equally bright and the reading

of the vernier on the circular scale is noted as 2' 'θ .

5) The difference between 1 2 andθ θ gives the angle of rotation ( )1 2~θ θ θ= produced by the solution.

6) The experiment is repeated with different known concentrations of the solution.

7) A graph is then plotted between concentrations and the angle of rotation, which results a straight line.

8) From the graph the ratio ' 'Cθ is determined. Substituting these values, the specific rotation is calculated by

using the formula, Sl C

θ=

×.

2) BI-QUARTZ POLARIMETER:

Bi-Quartz polarimeter is an accurate instrument which is more sensitive than half-shade polarimeter.

The experimental set-up is same as that of half-shade polarimeter except tha half-shade device is replaced by

Bi-quartz device and monochromatic

light is replaced by white light.

Construction: The essential parts

of a Bi-quartz polarimeter are as shown

in the figure. S is a white light source

and L is a convex lens which makes the

incident rays into parallel beam. N1 and

N2 are two Nicol Prisms. N1 acts as a

Polarizer and N2 acts as an Analyzer. N2 is capable of rotating about an axis through N1 and N2. The rotation of the

analyzer can be read from the graduated circular scale C.S. The light after passing through the N1 is allowed to pass

through Bi-quartz device (B.Q.) and then through a glass tube T which holds the optically active substance (here sugar

solution). The glass tube T is a hallow tube having a large diameter in the middle so that no air bubble may be in the

path of the light when filled with liquid. It is also closed at the ends by over-slips and metal covers. The ray after

passing through the N2 is viewed by a telescope.

Bi-quartz Device: It consists of two semi-circular plates of quartz (one of left-handed quartz ‘L’ and other

right-handed quartz R) each of thickness 3.75mm. Both are cut perpendicular to the optic axis and joined together

along the diameter PQ’ as shown in figure. The thickness of each plate 3.75mm rotates the plane of polarization for

yellow light by 90o.

Action of Bi-quartz device: When white light after passing the polarizer travels through the bi-quartz normally,

the phenomenon of rotator dispersion occurs in both Bi-quartz plates because the plane of

polarized light is travelling along optic axis. The planes of vibration of different colours

are rotated through different angles. The rotation of Yellow colour is 90o and hence YOY is

a straight line.

If the principal plane of the analyzer is parallel to POQ, the Yellow light will not

be transmitted through the analyzer and the appearance of the two halves is grayish violet

tint, called as sensitive tint. When the analyzer is rotated to one side from this position one

half appears Blue while the other appears Red.

If the analyzer is rotated in opposite direction, then the colours are altered i.e., the

first Blue-half appears Red and the Red-half appears Blue. This position of sensitive tint is very sensitive and is used

for the accurate determination of optical rotation.

Determination of Specific Rotation: To determine the Specific rotation ‘S’ of a substance, a solution of known

concentration is prepared. The length of the solution is measured directly and the value of ' 'θ is determined as follows:

1) The glass tube is filled with water and placed in its proper position. 2) The telescope is focused on the Bi-quartz device and analyzer is rotated till Yellow colour position is

obtained and the reading of the vernier on the circular scale is noted as 1' 'θ .

3) Now the glass tube is filled with the optically active solution whose concentration is known and placed in its

proper position. The field of view in this stage will not be Yellow but a grayish violet tint is observed.

G

Y

R

P

90o

R

B

V Q

O

B

90o

G

Y

V

, Source S

1NBi quartz−

( . .)device H S

' 'Glass Tube T2N

Polarizer Analyzer ' 'Convex lens L

S

Circular( . .)Scale C S

Telescope

. F ig B i quartz P olarim eter−

White Light




4) The analyzer is rotated and is brought to a position so that the field of view is Yellow and the reading of the

vernier on the circular scale is noted as 2' 'θ .

5) The difference between 1 2 andθ θ gives the angle of rotation ( )1 2~θ θ θ= produced by the solution.

6) The experiment is repeated with different known concentrations of the solution.

7) A graph is then plotted between concentrations and the angle of rotation, which results a straight line.

8) From the graph the ratio ' 'Cθ is determined. Substituting these values, the specific rotation is calculated by

using the formula, Sl C

θ=

×.

Polarization of Light by Mr. Charis

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