As shown in the figure, three identical polaroids P₁, P₂ and P₃ are placed one after another. The pass axis of P₂ and P₃ are inclined at angle of 60° and 90° with respect to axis of P₁. The source S has an intensity of 256 W/m². The intensity of light at point O is ____________ W/m².

Solution

Physics sir · 4 steps

Malus's law needs the angle between neighbouring polaroids, so P3 is only 30° away from P2.

1. First polaroid. The source light is unpolarised, so P₁ lets through half of it: 256/2 = 128 W m⁻².

   I = I₀ cos² θ

2. Second polaroid. P₂ is at 60° to P₁, so by Malus's law I = 128 cos² 60° = 128 × 1/4 = 32 W m⁻².
3. Third polaroid. P₃ is at 90° to P₁, so it is at 90° - 60° = 30° to P₂. Then I = 32 cos² 30° = 32 × 3/4 = 24 W m⁻².
4. So. The intensity of light at O is 24 W m⁻².

The common slip: 0. Taking 90° as the angle between P₂ and P₃ gives 0. That 90° is measured from P₁, and the angle from P₂ is only 30°.

The idea to keep. Halve the intensity at the first polaroid for unpolarised light. After that, use cos² θ with the angle between each polaroid and the one just before it, not the first one.

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