A linearly polarized electromagnetic wave is sent through two sheets of polarizi

Question

A linearly polarized electromagnetic wave is sent through two sheets of polarizing material. The first sheet, A, is oriented so that its transmission axis makes an angle of 30 degree with respect to the incident electric field of the wave. The second sheet, B, is oriented so that its transmission axis makes an angle of 90 degree with the incident electric field of the wave. The incident beam has an electric field of peak magnitude E_0 and average intensity S_0. What is the average intensity of the wave after it passes through B? A) 0.1 S_0 B) 0.34 S_0 C) 0.43 S_0 D) 0.50 S_0 E) zero

Explanation / Answer

the first polarizer passes light parallel to the axis of the polarizer. THis is the projection of the incident S field on the polarizer's axis.

Sa = So*cos(30) = sqrt(3)/2*So

The intensity is the square of the S field: Ia = Sa^2 = 3/4*So^2

Now Sa is at an angle of 60 deg with respect to polarizer B so the field passing through is:

Sb = Sa*cos(60) = 1/2*Sa = sqrt(3)/4*So

Average intensity is Ib = 3/16*So = 0.1875So = 0.19So (approx)

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