A beam of unpolarised light of intensity I₀ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45° relative to that of A. The intensity of emergent light is:

Solution

Physics sir · 3 steps

Two stages here: the first polaroid halves the light, then Malus' law handles the 45° tilt.

1. Through polaroid A. Unpolarised light vibrates in every direction equally, so a polaroid passes the average of cos² θ over all angles, which is 1/2. The light leaving A has intensity I₀/2 and is now polarised along A's axis.
2. Through polaroid B. This light is already polarised, so Malus' law applies with θ = 45° between the two axes.

   I = I₀/2 cos² 45° = I₀/2 × 1/2 = I₀/4

3. So. The emergent intensity is I₀/4, option (c).

The idea to keep. For unpolarised light, the first polaroid always gives half the intensity, whatever its angle. Use Malus' law I = I'cos² θ only from the second polaroid onwards.

Answer from the NTA final answer key. Solution by PrepWiser.