Two Polaroid A and B are placed in such a way that the pass – axis of Polaroids are perpendicular to each other. Now, another Polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarized light is $I_0$ then intensity of transmitted light after passing through Polaroid B will be:

Given Polaroids, A and B are at an angle of 90⁰. A 3rd polaroid C is placed bisecting A and B. 

Therefore angle between A and C is 45⁰ and angle between C and B is 45⁰.

Intensity of unpolarized light is I₀ 

Intensity of transmitted light after passing through Polaroid A is

${\mathrm{I}}_{\mathrm{A}}=\frac{{\mathrm{I}}_0}{2}$

Intensity of transmitted light after passing through Polaroid C is

${\mathrm{I}}_{\mathrm{C}}={\mathrm{I}}_{\mathrm{A}}{\cos }^2\mathrm{\theta }=\frac{{\mathrm{I}}_0}{4}$

Intensity of transmitted light after passing through Polaroid B is

${\mathrm{I}}_{\mathrm{B}}=\frac{{\mathrm{I}}_0}{4}{\cos }^2\frac{\mathrm{\pi }}{4}=\frac{{\mathrm{I}}_0}{8}$