Question

Unpolarized light of intensity $32\frac{W}{m^2}$ passes through three polarizers such that the transmission axis of the last polarizer is crossed with that of the first. The intensity of final emerging light is $3\frac{W}{m^2}$ . The angle between the first two transmission axes of the polarizers is:

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

Answer 1

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

$32\to 16\left(A\right)\to 16{\cos }^2\theta \left(B\right)\to 16{\cos }^2\theta {\sin }^2\theta \left(C\right)$

$\Rightarrow 16{\cos }^2\theta {\sin }^2\theta =3$
$\Rightarrow \frac{16}{4}\times 4{\cos }^2\theta {\sin }^2\theta =3$
$\Rightarrow 4\times {\sin }^{2}2\theta =3$
On solving we get $\theta$ as ${30}^{\circ }$