Question

When does intensity become maximum when a polariod sheet isrotated between two crossed polaroids?

Answer 1

I1 = Io cos^2 x    where x is the angle between  2 crossed polaroids

I2 = I1 cos^2 y     transmission thru second polaroid   where y = 90 - x

or I2 = I1 sin^2 x      since cos (90 - x) = sin x

I = Io cos^2 x sin^2 x

1 / Io * dI / dx = -2 sin^2 x sin x cos x + 2 cos^2 x sin x cos x = 0

sin^3 x cos x = cos^3 x sin x

tan^3 x = tan x

tan^2 x = 1      

cos^2 x = sin ^2 x    and cos x = sin x

Then maximum occurs when the sheet is at 45 degrees