Unpolarized light of intensity  $32W{m}^{-2}$ passes through three polarizers such that the transmission axis of the last polarized is crossed with the first. If the intensity of the emerging 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.
   $\theta +\varphi ={90}^{0}or=({90}^0-0)$                                ……(1)
Now if $I_0$  is the intensity of unpolarized light incident on Polaroid  $P_1$, the intensity of light transmitter through it, 
 $I_1=\frac{1}{2}{I}_0=\frac{1}{2}\left(32\right)=16\frac{W}{m^2}$   ……..(2)
Now as angle between transmission axes of Polaroid  $P_1$  and $P_2$  is $\theta$ , in accordance with malus law, intensity of light transmitted through $P_2$  will be
$I_2=I_1{\cos }^2\theta =16{\cos }^2\theta$     …..(3)
And as angle between transmission axes of $P_2$   and $P_2$  is $\varphi$ , light transmitted through  $P_3$ will be 
  $I_3=I_2{\cos }^2\varphi =16{\cos }^2\theta {\cos }^2\varphi$  ….(4)
According to given problem,  $I_3=3W/m^2$
So,  $4{\left(\sin 2\theta \right)}^2=3i.e,\sin 2\theta =(\sqrt{3}/2)\left(or\right)2\theta ={60}^{0}i.e.,\theta ={30}^0$