we know that a transverse EM wave contains both electric and magnetic field and electric field in light wave is perpendicular to the direction of propagation of light wave

We generally define direction of light vibration to be that of the electric vector E

For an ordinary unpolarised beam electric vector keeps changing its direction in random manner

when light is allowed to pass through a Polaroid the emergent light is plane polarized with its electric vector vibrating in a particular direction

The direction of vector of emergent beam depends on the orientation of the Polaroid and the plane of polarization is designed as the plane containing E-vector and light ray

Figure below shows the plane polarized light due to i) a vertical E-vector ii) a horizontal E-vector

9)Law of Malus

consider the figure given below in which an unpolarized light passes through a Polaroid P_{1} and then through Polaroid P_{2} making an angle Î¸ with y ax-s

After light propagating along x-direction passes through the Polaroid P_{1} ,the electric vector associated with the polarized light will vibrate only along y-axis

Now if we allow this polarized beam to again pass through a polarized P_{2} making an angle Î¸ with y-axis then if E_{0} is the amplitude of incident electric field on P_{2} then amplitude of wave emerging from P_{2} would be E_{0}cosÎ¸ and hence intensity of emerging beam would be

I=I_{0}cos^{2}Î¸ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ---(4)

where I_{0} is the intensity of beam emerging from P_{2} when Î¸=0

This equation (4) represents the law of malus

Thus when a plane polarized light is incident on an analyzer ,the emerging light varies in accordance with the equation (4) where Î¸ is the angle between the planes of transmission of the analyzer and the polarizer

10) Brewster's law

Brewster law is a simple relationship between angle of maximum polarization and the refractive index of the medium

Brewster’s law is given by relationship
Î¼=tani Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â --(5)

where i is the Polarizing angle
Î¼is the index of refraction
It is clear from equation (5) that when light is incident at polarizing angle then reflected ray is at right angles to the reflected ray