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. ${60}^{\circ }$
• B. $0^{\circ }$
• C. ${30}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

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


From figure, it can be seen that the pass axis of $A$ and $B$ are parallel.

When polarizer $C$ is introduced between $A$ and $B$:


Intensity of plane polarized light when passed through $C$

$I^{\prime }=\frac{I}{2}{\cos }^2\theta ....\left(1\right)$

Intensity of light when passed through $B$

$I^{\prime \prime }=I^{\prime }{\cos }^2\theta$

but $I^{\prime \prime }=\frac{I}{8}$

$\therefore \frac{I}{8}=\frac{I}{2}{\cos }^2\theta \times {\cos }^2\theta \left[\text{from eqn}\right(1\left)\right]$

$\Rightarrow {\cos }^4\theta =\frac{1}{4}$

$\Rightarrow \cos \theta =\pm \frac{1}{\sqrt{2}}$

$\therefore \theta ={45}^{\circ }\text{or}\theta ={135}^{\circ }$

Hence, option $\left(\text{D}\right)$ is correct.