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Two Polaroid sheets are arranged in the path of an unpolarized beam of intensity I0 so that the second sheet transmits no light. If a third Polaroid is inserted between them, and its transmission axis makes an angle θ with the axis of the first Polaroid, what is the intensity of the light emerging from the final Polaroid?
- (I0 / 8) sin² 2θ
- (I0 / 4) sin² 2θ
- (I0 / 8) cos⁴ θ
- I0 cos⁴ θ
Correct answer: (I0 / 8) sin² 2θ
Solution
After the first sheet intensity is I0/2. The middle sheet (axis at theta) gives (I0/2)cos^2(theta); the last sheet is at 90-theta to it, giving (I0/2)cos^2(theta)*sin^2(theta) = (I0/8)sin^2(2theta).
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