An unpolarised light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30° in clockwise direction, the intensity of emerging light will be _________ Lumens.

Solution

Physics sir · 3 steps

The 100 lumens is the aligned reading, so turning the analyzer by 30° just multiplies it by cos²30°.

1. Starting reading. The polarizer passes half of the unpolarised light. The analyzer then gives 100 lumens, which this question takes as the reading with the analyzer axis parallel to the polarizer axis. So the light reaching the analyzer, already polarised, carries I₀ = 100 lumens.
2. Apply Malus law. Rotating the analyzer by 30° makes the angle between the two axes θ = 30°. The direction of rotation does not matter, because cos² θ is the same for clockwise and anticlockwise turns.

   I = I₀cos² θ = 100 × cos² 30° = 100 × 3/4

3. So. The emerging intensity is 75 lumens.

The common slip: 25. Using sin² 30° instead of cos² 30° gives 25. Malus law uses the cosine of the angle between the two axes.

The idea to keep. The halving happens only once, at the first polarizer. After that, every polarizer or analyzer multiplies the intensity by cos² of the angle between its axis and the light's plane of polarisation.

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