A third polaroid is inserted between two crossed polaroids (90° apart). If the middle polaroid's pass-axis is at angle θ to the first polaroid, the transmitted intensity (after the third polaroid) is maximum when:
Aθ = 0°
Bθ = 30°
Cθ = 45° (transmitted I = (I₀/4) sin²(2θ), max at θ = 45°)
Dθ = 90°
Answer & Solution
Correct answer: C. θ = 45° (transmitted I = (I₀/4) sin²(2θ), max at θ = 45°)
After polaroid 1 (with unpolarised input I₀): I = I₀/2. After polaroid 2 at angle θ: I = (I₀/2) cos²θ. After polaroid 3 perpendicular to P₁ (so at angle 90°−θ to P₂): I = (I₀/2) cos²θ × cos²(90°−θ) = (I₀/2) cos²θ sin²θ = **(I₀/8) sin²(2θ)**. Max when 2θ = 90° → **θ = 45°**.
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