1

Polarization

1

Polarisation

XY – Plane: Plane of polarisation

S =(E x B)/μo

Unpolarized light

Polaroid: Transmits along the pass axis and absorbs along the perpendicular axis

Malus law 222 cos)cos( oo IEEI

Unpolarized light2

cos2 oo

III

Degree of polarisationIf the incident light is a mixture of unpolarised light of intensity Iuand polarised light of intensity Ip, then the transmitted light is given by:

2cos2 pu I

II

2 ;

2 minmaxu

pu I

III

I

minmax

minmax

II

IIP

Polarisation by scattering

Rayleigh scattering

Blue sky

Red Sunset / Sunrise

Convention

- Polarisation

Plane of polarisation is same as plane of incidence

- Polarisation

Plane of polarisation is perpendicular to the plane of incidence

Polarisation by reflection

Brewster angle

Glasspartially polarised

linearly polarised

unpolarised polarised

Brewster angle

= Brewster angle

Brewster’s law

Polarisation by reflection

Polarisation by double refraction- Two refracted beams emerge instead of one- Two images instead of one

Calcite Quartz

Optic Axis: Uniaxial crystals exhibit cylindrical symmetry. There is a unique direction in a uniaxial crystal called the optic axis.Values of physical parameters along optic axis are different from the values perpendicular to it.

Calcite

Extraordinary rayOrdinary ray

Optic axisPrincipalPlane:

Plane contains optic axis and the

direction of propagation

CalcitePolariser/Analyser

Ordinary rayσ - polarised

Extraordinary rayπ - polarised

Calcite

Polarisation by double refraction

Isotropic Medium : Velocity Spherical

Uniaxial and Biaxial CrystalsUniaxial : Calcite, Quartz

Biaxial: Mica

Anisotropic Medium : Velocity ellipsoid

- PolarisationPlane of polarisation is same as

plane of incidence (principal plane)

- PolarisationPlane of polarisation is perpendicular

to the plane of incidence (principal plane)

Plane of incidence : plane contains incident ray, reflected/refracted ray, surface normal

Plane of polarisation : plane contains electric field vector and direction of propagation

Principal plane : Plane contains optic axis and the direction of propagation

This definitionis considered in absence of Principal Plane

e-ray : Plane of polarisation is same as principal plane

Plane of polarisation is perpendicular to the principal plane

o-ray :

e-ray in general does not obey the laws of refraction except in case of special cut of crystal (optic axis)

o-ray always obeys the laws of refraction

Always e-ray carries -polarisation and o-ray carries -polarisation

Positive and Negative uniaxial crystals

Quartz - Positive (ne - no)>0

Calcite - Negative (ne - no)<0

no = 1.5443 ne = 1.5534

ne = 1.4864no = 1.6584

For sodium D lines

Linear polarisation by double refraction

ne > no

ve < vo

Velocity or Refractive index is the same along the OPTIC AXIS for o-ray and e-ray.

ne < no

ve > vo

QuartzPositive crystal

Sphere

Spheroid

Wave surface is the locus of all points reached by the ray at a given instant

Velocity ellipsoid

ne > no

ve < vo

Sphere

Spheroid

ne > no

ve < vo

QuartzPositive crystal

Sphere

Spheroid

ne > no

ve < vo

QuartzPositive crystal

Calcite Negative crystal

Sphere

Spheroid

ne < no

ve > vo

Sphere

Spheroid

ne < no

ve > vo

Calcite Negative crystal

Sphere

Spheroidne < no

ve > vo

Calcite Negative crystal

Biaxial

Huygens’construction

Calcite ne < no

ve > vo

Special cuts of uniaxial crystalOptic axis normal to the surface of incidence

No double refraction

Optic axis parallel to the surface of incidence

No double refraction

Oblique IncidenceOptic axis parallel to the surface of incidence, normal to the plane of incidence

Nicol prism

Calcite

Canada balsamn = 1.55

no = 1.6584ne = 1.4864

Rochon prism

Wollaston prism

Elliptical and circular polarisation

Plane polarised

Circularly polarised

Etc.

Production of elliptically polarised light

O

E A O =

E =

Retarders

Quarter wave, Half wave and Full wave

GLASS

Quartz

Quartz

Half wave plate

Variable retarder

Babinet Compensatoris a

. . . . . .

. . . . . . . . . . . . . .. . . . . . . . .

C

))((2

21 eoo

nndd

Interference of polarised light

Fresnel-Arago laws

1. Two coherent rays polarised at right angles do not interfere

2. Two parallel coherent polarised rays will interfere in the same way as will ordinary light

Optically active medium

Specific rotation= 21.72 Deg/mmfor Sodium lines

Rotation of the plane of vibration & Rotatary dispersionDextrorotatary or right handed mediumLevorotatary or left handed medium

Sugar, Glucose and Fructose

Sugar (Sucrose or Cane sugar)

Glucose-D ( Dextrose or Grape sugar)

Fructose (Levulose or Fruit sugar)

Specific rotation

52.7

66.47

- 92

o

o

o

Specific rotation is defined as the observed rotation of light of wavelength 589 nm (the d line of a

sodium lamp) passing through 10 cm of a 1 g ml-1 solution of a sample.

Rotation in liquids

One can find out the density of substance in solution

[ρ] = 10 θ / ldSpecific rotation,

θ = angle of rotationl = Length of the liquid column in cmd = density in gm/cm3

Fresnel’s explanation of rotation

Induced Optical Effects

Isotropic medium can be made optically anisotropic applying

1. Stress : Photoelastic Effect2. Magnetic field : Faraday Effect3. Electric field : Kerr effect

Faraday effect

B

d

=Verdet cosntant

0.00001-0.01 min/Gauss-cm

Kerr effect

An isotropic medium becomes birefringent by an application of electric field.

It behaves like an uniaxial crystal with optic axis in the direction of applied field.

K = Kerr Constant