Chapter four

Polarization of light

Introduction

Nature light is transverse electromagnetic wave propagating in all direction generally is

named unpolarized light. Polarized light is propagate in only one plane.

The electric component (E) of wave light is said to be light vector because it cause the

sensation of vision and photographic action.

Polarizer is device used to converting the nature light into polarized light.

Analyzer is device can be used to investigate the degree of polarization.

Methods of polarization:- the methods used to produce the polarization of light are

1- Polarization by reflection 2- Dichorism 3- double refraction

4- transmission through a pile of plates 5- Scattering

polarized unpolarized

Polarization by Dichroism

Some crystals (Tourmaline, Calcite and Quartz) have the property

of selective absorbing all light rays vibrating in all direction

except parallel to its pass direction (optical axis) are completely

transmitted. (Dichroism Phenomena)

Dichroic crystal belong to the class of optical anisotropic media

(i.e. their physical properties change with measurement

direction)

Law of Malus

When a second polarizer is rotated, the vector

component perpendicular to its transmission plane is

absorbed, reducing its amplitude.

Since the transmitted intensity is proportional to the

amplitude squared, the intensity is given by:

20 CosII

Very important notice when solve the problems

To calculate the intensity by using mauls law the angle takes between next and previous sheets

(Polaroid)

The natural light intensity from 1st sheet =I0/2

For examples

I1 I

2 I = I

3

Io I

E What happens to

the intensity, I, and axis of polarization

of unpolarized light upon passing

through three polarizers (fig.) ?

2/01 II

25cos2

12 II

45cos

)2570(cos

2

2

2

23

I

II

0

22

03 205.045cos25cos2/1 III

Without the second polarizer:

0

2

03 058.070cos2/1 III

Polarization by Reflection

When unpolarized light incident on glass plate, the reflected

light from the surface is fully or partially polarized.

At certain incidence angle (polarizing angle) the reflected

light is fully plane polarized.

Brewster discovered that at the polarizing angle the reflected

and refracted rays are at right angle (90o)

Using Snell’s law

iii

ri

CosniSinnSinn

SinnSinn

221

21

)90(

12tan nnCosSin iii

Where n is refractive index of medium

Polarization by Refraction

(Polarization by transmission through a pile of plates)

Consider an ordinary light incident at the polarizing angle on a pile of plates, the degree of

polarization (P) of transmitted light is given by

2

21

2

n

nm

m

II

IIP

np

np

Where Ip is the intensity of the transmitted parallel component, In is the intensity of the normal

component, m is the number of plates in the pile and n is their refractive index.

Polarization by Double refraction

When ordinary light fall at normal incidence on one face

of the crystal, two refracted beams of light were

observed{ordinary beam(O) and Extraordinary

beam(E)}

. there are two beams the velocity of O beam is the same

in all directions (wave front spherical) and velocity of E

beam varies with direction ( wave front spheroidal)

Optical axis of crystal is the axis in crystal for which

the two surfaces intersect(O&E)

Negative crystal

(crystal for which Vo < VE) or (crystal for which

no < nE)

Positive Crystal

(crystal for which Vo >VE) or (crystal for which no > nE)

o-ray

e-ray

1)/(tan 2 Eo nnd

y

o

E

n

n

L

d cos

Problem of Polarization

1- The magnetic field equations for an electromagnetic wave in free space are Bx =Bo sin (t + kZ),

By= Bz = o. (a) What is the direction of wave propagation? (b) Write the electric field equations.

(c) Is the wave polarized? If so, in what direction? Draw.

Answer

00 zyox BBkZtSinBB

(a) the direction of wave propagation is negative direction of Y-

axis

00

xz

oy

EE

kztSinEE

(c) This wave is polarized

plane Z-X in theB

plane Z-Y in theE

2- An unpolarized beam of light is incident on a group of four

polarizing sheets that are lined up so that the pass direction of each is rotated by 300 clockwise with respect to

the preceding sheet.

Calculate the fraction of the incident intensity that is transmitted.

Answer

2CosII o

21 oII

8

330

2 0

2202

12 I

ICos

ICosII

32

930

2

1402

23 oI

ICos

ICosII

128

2730

2

4602

34 oI

ICos

ICosII

4- An ordinary beam of light is sent through three dichroic polarizers, the 2nd of which is oriented at 250

with the first and the 3rd at 500 with the first in the same direction. Calculate the intensity that gets through

the system relative to that of the incident beam, (a) neglecting light ret1ected from the six surfaces, and (b)

assuming 4% of the light ret1ected at each surface.

Answer

(a)- no reflection 2CosII o 21 oII

41.0252 0

2202

12 I

ICos

ICosII

387.0252

3402

23 oI

ICos

ICosII

4% of light is reflected

%4848.0200

96)2(

100

96 1

1 o

oI

III

%8.37378.025100

9648.0

100

96

0

222

12 I

ICosICosII o

%8.29298.025100

96378.0

100

96

0

322

23 I

ICosICosII o

6- How would you orient the polarizer and the analyzer so that a beam of natural light is reduced to (a)

1/2, (b) 1/4 and (c) 1/8 of its original intensity?

Answer

a) 21 oII

20

22

CosI

I 22

2

1Cos

I

I

o

When = 90o 02 oI

I

The angle between polarizer and analyzer is 90o

2

1

2

1

4

1 222 CosCosI

I

o

452

1

2

1 1

CosCos

c)

4

1

2

1

8

1 222 CosCosI

I

o

602

1

4

1 1

CosCos

7- A double refracting crystal made of nitrate of soda has for normal incidence of sodium light nO = 1.58 and

nE = 1.461. for a crystal with thickness 1 cm, calculate the linear separation between 0 and E rays as they

emerge from the crystal.

Answer

d

L

n

n

E

o dn

nL

E

o and

1)/( 2 Eo nndy

)1)461.1/585.1(5.2 2 y

d =0.42 cm

8- Find the angular separation of 0 and E rays obtained in a tourmaline crystal for sodium light. Consider

normal incidence of light and nO = 1.64, nE = 1.63

Answer

63.164.1? Eo nn

1)/(tan 2 Eo nnd

y

1)63.1/64.1(tan 2

1109.0tan

o33.6