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° 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° with the incident electric field of the wave. The incident beam has an electric field of peak magnitude Eo and average intensity So what is the average intensity of the wave after it passes through A?

Explanation / Answer

The first polarizer passes light parallel to the axis of the polarizer. This is the projection of the incident E field on the polarizer's axis.

Ea = E0*cos(30) = sqrt(3)/2*E0

The intensity is the square of the E field: Ia = Ea^2 = 3/4*E0^2

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

Eb = Ea*cos(60) =1/2*Ea =sqrt(3)/4*E0

Average intensity is Ib = 3/16*E0

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