A third ideal polaroid is inserted between two crossed polaroids with its transmission axis at 22.5° to the first. If I₀ is the light intensity after the first polaroid, what intensity emerges after the third?
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Question

A third ideal polaroid is inserted between two crossed polaroids with its transmission axis at 22.5° to the first. If I₀ is the light intensity after the first polaroid, what intensity emerges after the third?

Options

G1 Physics · Accepted Answer

Step 1: The original polarizer and analyzer axes are 90° apart. The intermediate polaroid is at θ = 22.5° from the first. Step 2: Malus’s law through the middle sheet: I₁ = I₀cos²θ. Step 3: Angle from the middle sheet to the crossed final analyzer is (90° − θ) = 67.5°. Step 4: Through final analyzer: I = I₁cos²(90° − θ) = I₀cos²θ sin²θ. Step 5: Use sin2θ = 2sinθcosθ: I = (I₀/4)sin²(2θ). Step 6: 2θ = 45°, hence I = (I₀/4)(1/2) = I₀/8. Final answer: I₀/8, Option C.