GR0877 Problem 16
PROBLEM STATEMENT: This problem is still being typed.
SOLUTION: (D) When unpolarized light passes through the first polarizer it loses one-half of its intensity. Why a half? Here is an explanation. A beam of unpolarized light is nothing but a uniform mixture of linear polarizations at all possible angles. When a polarized beam of light of intensity is incident on a perfect polarizer, the intensity of light that passes through is (Malus’s law). Averaging this over all possible angles and using the fact that the average of is 1/2 (to prove, average the identity over one cycle), one has: , where is the intensity of light after the first polarizer. After the first polarizer the light is linearly polarized and the fraction of light that passes through the second polarizer is given by (again, using Malus’s law): or 25%.
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