An unpolarised beam of light of intensity I_0 falls on a single polar…

The correct answer is Option (1) → \( I_0/2 \)

Unpolarised light has electric field vectors in all directions perpendicular to the ray. A polaroid passes only the component along its pass axis, so by Malus's law each component is reduced by \( \cos^{2}\theta \).

    \( \displaystyle I = I_0\,\langle\cos^{2}\theta\rangle = I_0 \times \frac{1}{2} = \frac{I_0}{2} \)

The average of \( \cos^{2}\theta \) over all orientations is \( 1/2 \). So the transmitted light is plane polarised with half the intensity of the incident beam.

NCERT (2026-27):
Polarisation – “… Thus, if an unpolarised light wave is incident on such a polaroid then the light wave will get linearly polarised with the electric vector oscillating along a direction perpendicular to the aligned molecules; this direction is known as the pass-axis of the polaroid. Thus, if the light from an ordinary source (like a sodium lamp) passes through a polaroid sheet P₁, it is observed that its intensity is reduced by half.”