Q 12-10-149JEE MainJEE Main 2018 (16 Apr, Shift 1)Medium
Unpolarized light of intensity $I$ is incident on a system of two polarizers, $A$ followed by $B$. The intensity of emergent light is $\dfrac I2$. If a third polarizer $C$ is placed between $A$ and $B$ the intensity of emergent light is reduced to $\dfrac I3$. The angle between the polarizers $A$ and $C$ is $\theta$, then
Answer: (A) $\cos\theta = \left(\dfrac23\right)^{1/4}$
After $A$ the intensity is $\dfrac I2$. Since $B$ passes all of it, the axes of $A$ and $B$ are parallel.
With $C$ at angle $\theta$ to $A$, it is also at $\theta$ to $B$:
$$\frac I2\cos^2\theta\cos^2\theta = \frac I3 \quad\Rightarrow\quad \cos^4\theta = \frac23 \quad\Rightarrow\quad \cos\theta = \left(\frac23\right)^{1/4}$$
Solution by Sreeraj P, M.Sc Physics