Question

Unpolarized light of intensity I passes through an ideal polariser A. Another identical polarizer $B$ is placed behind $A$. The intensity of light beyond B is found to be $\frac{I}{2}$. Now another identical polarizer $C$ is placed between A and B. The intensity beyond $B$ is now found to be $\frac{I}{8}$. The angle between polarizer $A$ and $C$ is :

• A. $0^{\circ }$
• B. $0^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

From given,
$\frac{I}{2}\left(A\right)\to \frac{I{\cos }^2\theta }{2}\left(B\right)\to \frac{I}{2}{\cos }^2\theta {\cos }^2\theta \left(C\right)=\frac{I}{8}\left(C\right)$

$\Rightarrow \frac{I}{2}{\cos }^2\theta {\cos }^2\theta =\frac{I}{8}$
$\Rightarrow \frac{I}{2}{\cos }^4\theta =\frac{I}{8}$
$\Rightarrow {\cos }^4\theta =\frac{1}{4}$
$\Rightarrow \cos \theta =\frac{1}{\sqrt{2}}$
$\theta ={45}^o$