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° with respect to its predecessor. The ratio of the intensity of the final emerging light to that of the unpolarised light is

$\frac{81}{512}$

The correct answer is Option (3) → $\frac{81}{512}$

Intensity of light after passing through first polariser is $\frac{I_0}{2}$

Intensity of light after crossing through another polariser is $ I = \frac{I_0}{2} cos^2\theta = \frac{I_0}{2} cos^2 30^o = \frac{3I_0}{8}$

The ratio of Intensity after passing through 5 polariser it becomes $ \frac{I}{I_0} =\frac{1}{2} (\frac{3}{4})^4 = \frac{81}{512}$.