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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