Question

Unpolarized light of intensity $32W{m}^{-2}$ passes through three polarisers such that the transmission axis of the last polarizer is perpendicular to that of the first. The intensity of final emerging light is $3W{m}^{-2}$. The angle between the transmission axes of the first two polarizers will

• A. ${10}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

$I_0=32W{m}^{-2}$
$I_2=I_{1}co{s}^2\theta$ . . . .(1)
$I_1=\frac{I_0}{2}$
$I_3=I_{2}co{s}^2(90-\theta )$ . . . .(2)
$I_3=I_{1}co{s}^2\theta si{n}^2\theta =\frac{I_0}{2\times 4}4si{n}^2\theta co{s}^2\theta$
$I_3=\frac{I_0}{8}(sin2\theta {)}^2$
$3=\frac{32}{8}(sin2\theta {)}^2;\sqrt{\frac{3}{4}}=sin2\theta$
$Sin2\theta =\frac{\sqrt{3}}{2}$ ; $2\theta ={60}^{\circ }$
$\theta ={30}^{\circ }$