Question

Unpolarized light of intensity $I$ passes through an ideal polarizer $A$. 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. $30^{\circ }$
• C. $45^{\circ }$
• D. $60^{\circ }$

Answer 1

Answer: (C)

Polaroids $A$ and $B$ are oriented with parallel pass axis
Let polaroid $C$ is at angle $\theta$ with $A$ then it makes $\theta$ with $B$ also.
$\frac{1}{8}=\left(\frac{1}{2}\times {\cos }^2\theta \right)\times {\cos }^2\theta$
$\Rightarrow {\cos }^2\theta =\frac{1}{2}$
$\Rightarrow \theta =45^{\circ }$