A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just $36\%$ of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser needs to be rotated further, to reduce the output intensity to zero, is: $\left(\sin^{-1}\left(\tfrac35\right) = 37^\circ\right)$
Answer: (B) $37^\circ$
By Malus' law, with $\theta$ the angle between the polarizer and analyser axes:
$$\cos^2\theta = 0.36 \Rightarrow \cos\theta = \frac35 \Rightarrow \theta = 53^\circ$$
The output is zero when $\theta = 90^\circ$, so the analyser must be turned further by
$$90^\circ - 53^\circ = 37^\circ$$
(The official answer key lists $53^\circ$, which is the present angle between the axes, not the further rotation asked for.)
Solution by Sreeraj P, M.Sc Physics