A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just 10% of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is :

Solution

Physics sir · 4 steps

Find the angle you are already at using Malus's law; zero output needs 90°, so only the gap is left.

1. Malus's law. Take I₀ as the intensity of the polarised light reaching the analyser. Nothing is absorbed, so the output depends only on the angle θ between the polarizer and analyser axes.

   I = I₀cos² θ = 0.1 I₀ ⇒ cos θ = √0.1 = 0.316

2. Present angle. θ = cos⁻¹(0.316) ≈ 71.6°. This is where the analyser sits right now.
3. Zero output. The output is zero only when cos θ = 0, that is at θ = 90°, when the axes are crossed. The analyser must turn by the remaining gap: 90° - 71.6° = 18.4°.
4. So. The analyser needs a further rotation of 18.4°, option (c).

The idea to keep. Malus's law gives the angle you are at now. When the question asks how much further to turn, subtract that angle from the target: 90° for darkness, 0° for maximum.

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