(a) Using the phenomenon of polarization, show how transverse nature of light can be demonstrated.

(b) Two Polaroid P₁ and P₂ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity Io is incident on P₁. A third Polaroid P₃ is kept in between P₁ and P₂ such that its pass axis makes an angle of 30^o with that of P₁. Determine the intensity of light transmitted through P₁, P₂ and P₃. 

a)
i. Light from a source S is allowed to fall normally on the flat surface of a thin plate of a tourmaline crystal, cut parallel to its axis. Only a part of this light is transmitted through A.
ii. If now the plate A is rotated, the character of transmitted light remains unchanged.
iii. Now another similar plate B is placed at some distance from A such that the axis of B is parallel to that of A.
iv. If the light transmitted through A is passed through B, the light is almost completely transmitted through B and no change is observed in the light coming out of B. 
 

v. If now the crystal A is kept fixed and B is gradually rotated in its own plane, the intensity of light emerging out of B decreases and becomes zero when the axis of B is perpendicular to that of A.
vi. If B is further rotated, the intensity begins to increase and becomes maximum when the axes of A and B are again parallel. Thus, we see that the intensity of light transmitted through B is maximum when axes of A and B are parallel and minimum when they are at right angles.
From this experiment, it is obvious that light waves are transverse and not longitudinal; because, if they were longitudinal, the rotation of crystal B would not produce any change in the intensity of light.

Intensity of light transmitted through P₁  = I_o/2

Intensity of light transmitted through P₃ = ( I_o / 2) cos ² 30^o = 3 I_o / 8

Intensity of light transmitted through P₂ =  3/8 I_o cos² 60^o = 3/32 I_o