An unpolarised light of intensity \( I_0 \) passes through five identical polarisers arranged in such a manner that the transmission axis of each is set at an angle of \( 30^\circ \) with respect to its predecessor. The ratio of the intensity of the final emerging light to that of the unpolarised light is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{81}{512} \)
The first polariser halves the intensity of unpolarised light, whatever its orientation. After that the light is polarised, and each further polariser obeys Malus's law, \( I = I'\cos^{2}\theta \).
\( \displaystyle I_1 = \frac{I_0}{2} \)
Each of the remaining four polarisers is at \( 30^\circ \) to the one before it:
\( \displaystyle \cos^{2}30^\circ = \left(\frac{\sqrt{3}}{2}\right)^{2} = \frac{3}{4} \)
\( \displaystyle I_5 = \frac{I_0}{2}\left(\frac{3}{4}\right)^{4} = \frac{I_0}{2}\times\frac{81}{256} = \frac{81}{512}\,I_0 \)
\( \displaystyle \frac{I_5}{I_0} = \frac{81}{512} \)