An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at $30^\circ$ and $90^\circ$, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at $60^\circ$ with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.
Answer: (C) $\dfrac{9}{4}$
Concept. Apply Malus's law at each polariser using the angle between successive axes.
Step 1. Without the third. $\dfrac I2\cos^260^\circ=\dfrac I8$.
Step 2. With it ($30^\circ$ then $30^\circ$). $\dfrac I2\cos^230^\circ\cos^230^\circ=\dfrac{9I}{32}$.
Step 3. Ratio. $\dfrac{9/32}{1/8}=\dfrac94$.
Answer. Option C.
Solution by Sreeraj P, M.Sc Physics
