A linearly polarized beam of light of intensity I 0 is propagating in the + z di

Question

A linearly polarized beam of light of intensity I0 is propagating in the +z direction and its direction of polarization makes an angle of 72° with the x-axis (the angle between the initial direction of polarization and the transmission axis of the first polarizer is 18° as described below). Two linear polarizing sheets are lined up perpendicular to the beam. The first sheet has its transmission axis at an angle 1 = 90° with respect to the x-axis. The transmission axis of the second is variable. (See lower panels of the figure.)

The second polarizer is set at various angles within the range 2 = 0 to 90° Calculate the intensity of the light after it has passed through the second polarizer for the following values of 2. Express each answer as a fraction of I1.

At 2 = 22° I2 / I1 =

Explanation / Answer

the intensity of light transmitted by the first polarizer is
Iy = I0 sin^2(72°)

The angle between the light incident on the second polarizer and the transmission axis of the second polarizer is (if I understand the problem correctly) (90° - q2). The intensity of light transmitted by the second polarizer is then
It = Iy cos^2(90° - q2) = I0 cos^2(18°) cos^2(90° - q2)
For q2 = 36°, It / I0 = cos^2(18°) cos^2(54°) =0.31

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