Brewsters Law

We can get polarized light from reflection according to Brewsters law which states that when a light incident on a glass slab at certain angle then, we can get the polarized light in reflected part polarized in direction perpendicular to plane of incidence. This particular angle is called polarizing angle and in this case the sum of angle of refraction and angle of polarization will be 90 i.e angle between reflected and refracted rays will be 90
p+r = 90
i.e r = 90
Now according to snell's lae
refractive index = sini/sinr
= sinp/sin(90-p)
= sinp/cosp
=tanp

Therefore refractive index of material is equal to tangent of polarizing angle.

Malus law
The intensity of the light coming out from analyzer will be directly proportional to the square of cosine of angle between polarizer and analyzer.
Now, if a be the amplitude of the light used and (theta) be the angle between analyzer and polarizer then acos(theta) will be the component of a along analyzer and asin(theta) will be that along perpendicular direction. Therefore intensity of light which pass through analyzer is
I = (acos(theta))^2
since a is constant
I α cos^2(theta)

Calcite crystal
It is a cuboid made up of six 119m having angle 109 and 71. There will be two corners in which all parallepgram will meet at obtuse angle are called blunt corners. The axis of crystal. The light incident on optical axis will pass without splitting. In actual practice light incident parallel to potical axis will pass without splitting. SO that optical axis is not just a line, it is a direction

Principal section
Principal section is a plane which contains optical axis and perpendicular to opposite faces

Quarter wave plate
A special type of crystal which introduces a path difference of λ/4(i.e quarter of wavelength) between two emergent light is called quarter wave plate
optical path for o-ray = Uot
optical path for e-ray = Uet

In case of clacite crystal UeUot - Uet = λ/4
In case of quarts crystal Ue>Uo
Uet - Uot = λ/4

Half wave plate
A special type of crystal which introduces path diference of λ/2(i.e) half of wave length) between two emergent light is called half wave plate
In case of clacite crystal UeUot - Uet = λ/2
In case of quarts crystal Ue>Uo
Uet - Uot = λ/2