Polarisation PPT

POLARIZATION

Only transverse waves may become polarized.

EM waves are periodic changes of

electric and magnetic fields in space and

time. EM waves is transverse waves.

ELECTROMAGNETIC WAVE: LIGHT

Techniques to obtained Polarised Light

1.Polarisation by Reflection

2.Polarisation by Refraction

3.Polarisation by Double Refraction

4.Polarisation by Scattering

Brewster’s Law

The tangent of the angle of polarization is numerically equal to

the refractive index of the medium.

pitan

ii X

Y

By Snell’s Law

r

ip

sin

sin

Comparing these two equations

r

i

i

i p

p

p

sin

sin

cos

sin

pir cossin

)90sin(sin p

o ir

o

pir 90

The maximum polarization (vibration in one plane only) of a ray

of light may be achieved by letting the ray fall on a surface of a

transparent medium in such a way that the refracted ray makes

an angle of 90° with the reflected ray

oXOY 90

Malus Law

When a completely plane –polarized light is incident on an

analyzer, the intensity of the emergent light varies as the

square of the cosine of the angle between the planes of

transmission of the analyzer and the polarizer.

The angle between the transmission axis of the analyzer and

the polarizer is θ. Eo is the amplitude of the electric vector

transmitted by the polarizer.

Intensity, Io of the light incident on the analyzer is

2

oo EI

The electric field vector E0 can be resolved into two rectangular

components i.e E0 cosθ and E0 sinθ.

The analyzer will transmit only the component ( i.e E0 cosθ )

which is parallel to its transmission axis. However, the component

E0sinθ will be absorbed by the analyser.

Therefore, the intensity of light transmitted by the analyzer.

2)cos( oEI

2cosoII

When θ = 90°, I = I0 cos290° = 0 That is the intensity of light

transmitted by the analyzer is minimum when the transmission

axes of the analyzer and polarizer are perpendicular to each

other.

When θ = 0° ( or 180° ), I = I0 cos2θ = I0 That is the intensity of

light transmitted by the analyzer is maximum when the

transmission axes of the analyzer and the polarizer are parallel.

DOUBLE REFRACTION

The splitting of unpolarised

light into two refracted

component (ordinary light

and extraordinary light)

travelling at different

speeds inside medium is

known as phenomenon of

double refraction.

This is observed

using a special crystal

category known as doubly

refracting crystal.

POSITIVE CRYSTAL (re < ro) AND NEGATIVE CRYSTAL (re > ro)

Properties of O ray and E-rays

Two different angle of refraction , i.e. re and ro

Both rays becomes parallel after emerging the

crystal

Ordinary follows the ordinary law of refraction

but not the extraordinary.

Both rays are plane polarised. Ordinary ray :

Plane of vibration is perpendicular to the

principal section while for extraordinary is

parallel to the principal section.

POSITIVE CRYSTAL (re < ro ; μe > μ0) AND

NEGATIVE CRYSTAL (re > ro; μ0 > μe)

The double refractive

property of calcite leads to

the formation of two images

as shown in these examples.

The images are related to the

existence of ordinary rays (o-

rays) and extraordinary rays

(e-rays). An analysis of these

rays shows that both these

rays are linearly polarized. Colorless Calcite Rhombohedron

with a long edge of ~12 cm.

DOUBLE REFRACTIVE CRYSTALS

Principal Section –

A plane containing the optic axis of

the crystal and perpendicular to the

two opposite refracting faces is

called principal section of the crystal

for that pair of faces:

Optic Axis – A line passing throgh any one of

the blunt corners and making equal angles

with each of three edges which meet at the

corner is known as optic axis

Birefringent devices – Separation

of the o- and e- rays.

Thin layer of

balsam cement

with μ= 1.55

For calcite, again, μe = 1.486, μo = 1.658

NICOL PRISM-Construction A calcite crystal that is cut,

polished, and painted,

separates the o-ray and e-

ray via TIR (total internal

reflection). A thin layer of

balsam glues two halves of

the crystal. Balsam has an

index of refraction, μb, which

is between that of the o- and

e-rays, i.e., μe < μb < μo.

Thus, the o-ray experiences

TIR at the balsam interface

and is absorbed by the layer

of black paint on the side.

The e-ray refracts normally

at the balsam interface an

leaves the crystal at the

bottom. Therefore, the

emitted ray can be used as a

fully linearly polarized beam.

o-ray absorping paint

e-ray

Air gap

This prism is similar

to the Nicol, prism but

without the use of

balsam cement.

NICOL PRISM - Working

Polarizers take advantage of double refraction and

total internal reflection

Combine two prisms of calcite, rotated so that the ordinary polarization in the first prism is extraordinary in the second (and vice versa).

The perpendicular polarization goes from high index (no) to low (ne) and undergoes total internal reflection, while the parallel polarization is transmitted near Brewster's angle.

Nicol Prism: made up from two prisms of calcite cemented with Canada balsam. The ordinary ray totally reflects off the prism boundary, leaving only the extraordinary ray.

Production of Polarised light

x=a cos (ωt)

y=b cos (ωt-δ)

2

2

2

2

2

sincos2

ab

xy

b

y

a

x

General eqution of Ellipse

PLANE POLARISED LIGHT IN A VERTICAL PLANE

The intersecting plane

looked at from the front.



PLANE POLARISED LIGHT IN A HORIZONTAL

PLANE

Superposition of plane-polarized waves. When two electromagnetic waves plane-polarized in

two perpendicular planes are present simultaneously

then the electric fields are added according to the rules

of vector addition, 'parallelogram rule' (superposition) .



Superposition of plane-polarized waves . The superposition of two waves that have the same

amplitude and wavelength and are polarized in two

perpendicular planes but there is a phase difference of

3π/2, 7π/2…… degrees between them. A phase difference

of 3π/2 or -90° means that when one wave is at its peak

then the other one is just crossing the zero line. Right

polarization.



CIRCULARLY POLARISED LIGHT: CLOCKWISE

Superposition of plane-polarized waves 3.

The following animation shows what happens when

the two waves shown on the previous page are

added with a phase difference of π/2, 5π/2 degrees



CIRCULARLY POLARISED LIGHT: ANTICLOCKWISE

Circular polarization

Circularly polarized waves The animations presenting the two types of circularly

polarized light are shown together so that you can compare

them more easily. •

Superposition of circularly polarized waves when a left circularly polarized wave and a right

circularly polarized wave are added.

• As we see, the result of superposing two

circularly polarized waves is a plane-

polarized wave.



Retardation Plates

1.Quarter Wave Plate A plate of a doubly refracting crystal where refracting

faces are cut parallel to the direction of optic axis

whose thickness is such that to produce a phase

difference of π/2 and a path difference of λ/4 between

the ordinary and extraordinry waves is called quarter

wave plate.

t=λ/4(μE ~ μo)

1.Half Wave Plate

t=λ/2(μE ~ μo)

Analysis of Polarised light

General Light

Rotating Nicol

No Intensity variation

Either circularly or unpolarised

Intensity variation with

min zero intensity

Plane Polarised

Intensity variation with min non-zero

intensity

Either elliptically or partially

plane polarised

Either circularly or unpolarised

Incident on quarter wave plate and then through

rotating nicol


min zero intensity

Circularly Polarised

No intensity variation

Unpolarised

Either Elliptically or partially polarised light

Incident on quarter wave plate and then through

rotating nicol


min zero intensity

Elliptically Polarised

Intensity variation with minimum non-

zero

Partially polarised

Optical Activity

Specific rotation

Polarimeters

LECTURES TO BE PREPARED BY

THE STUDENTS

L-13 & L-14

Consider hypothetical point sources of natural light embedded within negative

and positive uniaxial crystals, as shown in the left and right figures.

The shape of the ellipsoids depends on sign of n (+ or -) as shown.

CALCITE CRYSTAL

Documents

Polarisation PPT