Unpolarized light of intensity $32W{m}^{-2}$ passes through three polarizers such that the transmission axis of the last polarizer is crossed with the first. If the intensity of the emerging light is  $3W{m}^{-2}$, what is the angle between the transmission axes of the first two polarizers? 

If  $\theta$ is the angle between the transmission axes of first Polaroid $P_1$ and second  $P_2$ while  $\varphi$  between the transmission axes of second polaroid $P_2$  and third  $P_3$, then according to given problem.
 
Now if $I_0$  is the intensity of unpolarized light incident on polaroid $P_1$ , the intensity of light transmitted through it,  $I_1=\frac{1}{2}{I}_0=\frac{1}{2}\left(32\right)=16\frac{W}{m^2}\mathrm{.....}\left(2\right)$
Now  as angle between transmission axes of polaroids  $P_1$ and $P_2$ is $\theta$, in accordance with Malus law, intensity of light transmitted through  $P_2$ will be $I_2=I_1{\cos }^2\theta =16{\cos }^2\theta -----\left(3\right)$
 And as angle between transmission axes of $P_2$ and  $P_3$ is  $\varphi$, light transmitted through $P_3$  will be 
 
According to given problem,  $I_3=3W/m^2$
So,  $4{\left(\sin 2\theta \right)}^2=3i.e.,\sin 2\theta =(\sqrt{3}/2)$ or,  $2\theta ={60}^{\circ }i.e.,\theta ={30}^{\circ }$