Unpolarized light of intensity $32 \mathrm{W} {\mathrm{m}}^{-2}$ passes through three polarizers arranged such that the transmission axes of the first and the last polarizer are at right angles. If the intensity of emerging light is $3 \mathrm{W} {\mathrm{m}}^{-2}$, then what is the angle (in degree) between the transmission axes of the first two polarizers?

Since unpolarized light is passing through the first polarizer, hence the intensity of light after crossing the first polarizer will be

$I_1=\frac{1}{2}{I}_0=16 \mathrm{W} {\mathrm{m}}^{-2}$

Let us assume that the angle between the transmission axis of the first and second polarizer is $\theta$, then from Malus law we can find out the intensity of light after it crosses the second polarizer.

$I_2=I_1{\cos }^2\theta =16{\cos }^2\theta$

Similarly, the intensity of light after crossing the third polarizer is

$I_3=I_2{\cos }^2\left(90°-\theta \right)=16{\cos }^2\theta {\sin }^2\theta$

$\Rightarrow I_3=16{\cos }^2\theta {\sin }^2\theta =3$

$\Rightarrow 4{\cos }^2\theta {\sin }^2\theta =\frac{3}{4}$

$\Rightarrow {\sin }^2\left(2\theta \right)=\frac{3}{4}$

$\theta =30°$