Polarization (quick review)

Longitudinal wave- has the same property with respect to any plane through its line of polarization.
Transverse waves- behaves differently in different planes. Light waves are transverse in nature and the viberation in them are at right angles to the direction in which wave is traveling.
Plane Polarized - Since the viberations constituting the beam of light are confined only to one definite plane through the axis of the beam, the light is generally said to be plane polarized. Properties of plane polarized light beam wrt two planes, one containing the viberation and other at right angles to it

Note that
  • Vibrations of polarized light are linear --- light is plane polarized 
  • Vibrations of polarized light are circular --- light is circularly polarized 
  • Vibrations of polarized light are elliptic --- light is elliptically polarized 
  • circular and elliptical vibrations are the resultant of two linear vibrations perpandicular to each other differing in phase by π/2. 
Polarization by reflection
  • It is the simplest method of obtaining plane polarized light. 
  • This method was first discovered by Etiennie Louis Malus.
  • When a beam of light is reflected from the surface of a transparent medium the reflected light is partially polarized and the degree of polarization varies with the angle of incidence.
  • Percentage of polarized light in reflected beam is greatest when it is incident at an angle known as angle of polarization for the medium which is equal to 57.5 degree for glass and varies slightly with the wavelength of incident light.
  • Complete polarization is possible only with monochromatic light.
  • Reflected light is said to be plane polarized in the plane of incident.
Brewster's Law
  • This Law states that there is a simple relation between the angle of maximum polarization and the refractive index of the medium. This relation known as Brewster's Law is given by
    μ=tan i
    where i is the angle of incidence
    and μ is the index of refraction
  • Using this law it can be showen that 'when light is incident at angle of maximum polarization the reflected ray is at right angles to the refracted ray. From Brewster's Law
    μ=tan i = (sin i)/(cos i)
    From Snell's Law
    μ = (sin i)/(sin r)
    where r is the angle of refraction
    Therefore , (sin i)/(cos i) = (sin i)/(sin r)
    (sin i)/(sin (90- i)) = (sin i)/(sin r)
    or we have
    this gives i+r=90 degree
    showing that at maximum angle of polarization reflected and refracted rays are at right angles.
  • Brewster's Law is obeyed even when light is reflected at the surface of rarer medium.
  • Light reflected from both the upper and lower surfaces of a glass plate will be polarized in the plane of incidence.
Double Refraction

  • Certain crystals split a ray of incident light into two refracted rays , one which gives the fixed image and follows all the laws of refraction and this ray is known as ordinary ray (o ray). Other ray gives an image that rotates with rotation of crystal and this ray is know as extra ordinary ray (e ray).
  • Both e and o rays are plane polarized.
  • When the crystal is rotated about the incident ray as an axis , the o-ray remains fixed but the e-ray revolves around it.
  • The index of refraction for e-ray is therefore a function of direction.
  • There is always one direction in the crystal for which there is no distinction between the o and e rays and this direction is called optic axis.
  • e ray and o ray are parallel to each other.
  • Plane of polarization of both e and o rays are at right angles to each other.
  • A class of crystals in which there is a single direction known as optic axis along which all waves are transmitted with one uniform velocities while in any other direction there are two velocities are called uni-axial crystals for example calcite and tourmaline crystals are uni-axial.
  • Crystals having two optical axis that is they have two directions of uniform velocity are bi-axial crystals for example topaz, mica etc. 
Law of Malus
  • Intensity of incident polarized ray is equal to the sum of the intensities of two refracted rays
    Io = a2sin2θ
    and , Ie = a2cos2θ

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