Explanation

(d) Let $I_{0}$ be the intensity of incident light
Then the intensity of light from the $1^{st}$ polaroid is
$I_{1} = \frac{I_{0}}{2}$
Intensity of light from the 2$^{nd}$ polaroid is
$I_{2} = I_{1}\cos^{2}{60{^\circ} = \frac{I_{0}}{2}\left( \frac{1}{2} \right)^{2} = \frac{I_{0}}{8}}$
Intensity of light from the 3$^{rd}$ polaroid is
$I_{3} = I_{2}\cos^{2}{60{^\circ} = \frac{I_{0}}{8}\left( \frac{1}{2} \right)^{2} = \frac{I_{0}}{32}}$
Intensity of light from the 4$^{th}$ polaroid is
$I_{4} = I_{3}\cos^{2}{60{^\circ} = \frac{I_{0}}{32}\left( \frac{1}{2} \right)^{2} = \frac{I_{0}}{128}}$
Intensity of light from the 5$^{th}$ polaroid is
$I_{5} = I_{4}\cos^{2}{60{^\circ} = \frac{I_{0}}{128}\left( \frac{1}{2} \right)^{2} = \frac{I_{0}}{512}}$
Therefore, the fraction of the incident light that passes through the system is
$\frac{I_{5}}{I_{0}} = \frac{1}{512}$