Polarization 1 1 1

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

Unpolarized light

Degree of polarisation If the incident light is a mixture of unpolarised light of intensity Iu and polarised light of intensity Ip, then the transmitted light is given by:

Polarisation by scattering

Rayleigh scattering Blue sky Red Sunset / Sunrise

Convention

Plane of polarisation is same as plane of incidence Plane of polarisation is perpendicular to the plane of incidence

Polarisation by reflection

unpolarised polarised Brewster angle unpolarised polarised linearly polarised partially polarised Glass

Brewster angle

Brewster’s law = Brewster angle

Polarisation by reflection

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

Plane contains optic axis and the direction of propagation Ordinary ray Extraordinary ray Principal Plane: Optic axis Plane contains optic axis and the direction of propagation Calcite

Ordinary ray σ - polarised Polariser/ Analyser Calcite

Extraordinary ray π - polarised Calcite

Polarisation by double refraction Isotropic Medium : Velocity Spherical Uniaxial and Biaxial Crystals Uniaxial : Calcite, Quartz Biaxial: Mica Anisotropic Medium : Velocity ellipsoid

- Polarisation - Polarisation Plane of polarisation is same as This definition is considered in absence of Principal Plane Plane of polarisation is same as plane of incidence (principal plane) - Polarisation Plane 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

Plane of polarisation is same as principal plane e-ray : Plane of polarisation is same as principal plane e-ray in general does not obey the laws of refraction except in case of special cut of crystal (optic axis) o-ray : Plane of polarisation is perpendicular to the principal plane o-ray always obeys the laws of refraction Always e-ray carries -polarisation and o-ray carries -polarisation

Calcite - Negative (ne - no)<0 no = 1.6584 ne = 1.4864 Linear polarisation by double refraction Positive and Negative uniaxial crystals Quartz - Positive (ne - no)>0 no = 1.5443 ne = 1.5534 ne > no ve < vo For sodium D lines Calcite - Negative (ne - no)<0 ne < no ve > vo no = 1.6584 ne = 1.4864 Velocity or Refractive index is the same along the OPTIC AXIS for o-ray and e-ray.

Velocity ellipsoid Quartz Positive crystal ne > no ve < vo Wave surface is the locus of all points reached by the ray at a given instant Velocity ellipsoid Positive crystal Quartz ne > no ve < vo Sphere Spheroid

Positive crystal Quartz ne > no ve < vo Sphere Spheroid

Positive crystal Quartz ne > no ve < vo Sphere Spheroid

Calcite Negative crystal ne < no ve > vo Spheroid Sphere

Calcite Negative crystal ne < no ve > vo Spheroid Sphere

Calcite Negative crystal ne < no ve > vo Spheroid Sphere

Biaxial

Huygens’ construction

Calcite ne < no ve > vo

Special cuts of uniaxial crystal Optic axis normal to the surface of incidence No double refraction

Optic axis parallel to the surface of incidence No double refraction

Oblique Incidence Optic axis parallel to the surface of incidence, normal to the plane of incidence

Nicol prism Calcite no = 1.6584 ne = 1.4864 Canada balsam n = 1.55

Rochon prism

Wollaston prism

Plane polarised Circularly polarised Elliptical and circular polarisation Plane polarised Etc. Circularly polarised

Production of elliptically polarised light

Retarders Quarter wave, Half wave and Full wave

GLASS

Quartz

Half wave plate Quartz

Babinet Compensator is a Variable retarder C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Interference of polarised light Fresnel-Arago laws 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 Rotation of the plane of vibration & Rotatary dispersion Dextrorotatary or right handed medium Levorotatary or left handed medium Specific rotation = 21.72 Deg/mm for Sodium lines

Sugar, Glucose and Fructose Specific rotation Sugar (Sucrose or Cane sugar) o 66.47 Glucose-D ( Dextrose or Grape sugar) o 52.7 Fructose (Levulose or Fruit sugar) o - 92

Rotation in liquids 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. One can find out the density of substance in solution Specific rotation, [ρ] = 10 θ / ld θ = angle of rotation l = Length of the liquid column in cm d = density in gm/cm3

Fresnel’s explanation of rotation

Induced Optical Effects Isotropic medium can be made optically anisotropic applying Stress : Photoelastic Effect Magnetic field : Faraday Effect Electric field : Kerr effect

Faraday effect d B 0.00001-0.01 min /Gauss-cm =Verdet cosntant

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