Two polarisers P₁ and P₂ are arranged so that no light is transmitted through them. A third polariser P₃ is inserted between P₁ and P₂. For maximum transmitted intensity through the three polarisers, the angle between P₂ and P₃ is:
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Question

Two polarisers P₁ and P₂ are arranged so that no light is transmitted through them. A third polariser P₃ is inserted between P₁ and P₂. For maximum transmitted intensity through the three polarisers, the angle between P₂ and P₃ is:

Options

G1 Physics · Accepted Answer

P₁ and P₂ are crossed, so the angle between their transmission axes is 90°. Let the angle between P₁ and P₃ be θ. Then the angle between P₃ and P₂ is 90°-θ. If the intensity after P₁ is I₀/2, then by Malus' law: I = (I₀/2)cos²θ · cos²(90°-θ) = (I₀/2)cos²θ sin²θ = (I₀/8)sin²2θ. For maximum intensity, sin²2θ = 1 ⇒ 2θ = 90° ⇒ θ = 45°. Hence P₃ must make 45° = π/4 with each of the crossed polarisers. Correct option: C.