Discuss the intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids?

Explanation

Consider that a light of intensity `I_0` emerges out from first polaroid `(P_1)` and passed through another polaroid `(P_2)`, inclined at an angle `theta` with `(P_1)`.
The intensity of the light will be `I_0 cos^2 theta`
Consider another Polaroid `(P_3)` kept crossed to first polaroid `(P_1)`.
Since the angle between `P_1 and P_3` is `(90^@ - 0)`, the intensity of light after passing from `P_3` will be `I_0 cos^(2) cos^2 (90^@ - theta)`
`I = (I_0 cos^2 theta) (I_0 cos^2 (90^@ - theta))`
`implies I = (I_0 cos^2 theta sin^2 theta) = ((I_0 sin^2 2 theta))/(4)`
Thus light emitted from the crossed polaroid will be maximum when both the polaroids are at `45^@`.