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Unpolarised light of amplitude a falls on a polariser, then passes to an analyser whose axis makes 45 deg with the polariser's axis. What is the amplitude of the light finally transmitted through the analyser?

1. a/2
2. a/2 (after polariser the amplitude becomes a/sqrt(2), then times cos45)
3. (sqrt(3)/2)a
4. (3/4)a

Correct answer: a/2

Solution

Unpolarised light of amplitude a passing through the polariser emerges with amplitude a/sqrt(2) (intensity halved). Passing through the analyser at 45 deg, the amplitude is multiplied by cos45 = 1/sqrt(2). Final amplitude = (a/sqrt(2))*(1/sqrt(2)) = a/2.

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