A plane polarized light is incident on a polariser with its pass axis making angle $\theta$ with $x$-axis. At four different values of $\theta$, $\theta = 8^\circ, 38^\circ, 188^\circ$ and $218^\circ$, the observed intensities are same. What is the angle between the direction of polarization and $x$-axis?
Answer: (A) $203^\circ$
By Malus's law, $I = I_0\cos^2(\theta - \varphi)$, where $\varphi$ is the polarization direction. Equal intensities at $8^\circ$ and $38^\circ$ require these angles to lie symmetrically about $\varphi$ (or about $\varphi + 90^\circ$), modulo $180^\circ$:
$$\varphi = \frac{8^\circ + 38^\circ}{2} + n\cdot90^\circ = 23^\circ + n\cdot90^\circ$$
The same holds for $188^\circ$ and $218^\circ$. The possible values are $23^\circ, 113^\circ, 203^\circ, 293^\circ$; of the options, only $203^\circ$ fits.
Solution by Sreeraj P, M.Sc Physics