Three polarizers, centered on a common axis and with their planes parallel to ea

Question

Three polarizers, centered on a common axis and with their planes parallel to each other, have transmission axes oriented at angles of theta_1, theta_2, and theta_3 from the vertical, as shown in the figure below. Light of intensity I_i polarized with its plane of polarization oriented vertically, is incident from the left onto the first polarizer. What is the ratio I_f/I_i of the final transmitted intensity to the incident intensity for the following configurations theta_1 = 45 degree, theta_2 = 90 degree, and theta_3 = 0 degree theta_1 = 0 degree, theta_2 = 45 degree, and theta_3 = 90 degree

Explanation / Answer

a) is easy because the final pair of polarizes are at right angles to each other, so no matter what the original orientation of the incoming light, these two will completely stop any transmission.

The ration If / Ii = 0 , nothing is transmitted

b) The first filter 1 has the same orientation as teh incoming light and so has no effect at all on the intensity.

2 reduces the intensity from k A^2 to k(A.cos45)^2 where k is a constant and A is the wave amplitude.

This means that the new intensity is 1/2 of the original ((cos 45)^2 = 1/2)

The transmitted wave, oriented at 45 to the vertical now hits the final filter 3 , which is at 45 to the wave! So it transmits some of it - at half intensity again.

If = Ii / 4

If / Ii = 1/4

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