a
(a)No light is emitted from the second polaroid, so \({P_1}\) and \({P_2}\) are perpendicular to each other
Let the initial intensity of light is \({I_0}\). So Intensity of light after transmission from first polaroid = \(\frac{{{I_0}}}{2}\).
Intensity of light emitted from \({P_3}\) \({I_1} = \frac{{{I_0}}}{2}{\cos ^2}\theta \)
Intensity of light transmitted from last polaroid i.e. from \({P_2} = {I_1}{\cos ^2}({90^o} - \theta )\)= \(\frac{{{I_0}}}{2}{\cos ^2}\theta .{\sin ^2}\theta \)
\( = \frac{{{I_0}}}{8}\)\({(2\sin \theta \cos \theta )^2}\)= \(\frac{{{I_0}}}{8}{\sin ^2}2\theta \).