Unpolarized light is passed through three polarizers numbered as #1, #2, and #3

Question

Unpolarized light is passed through three polarizers numbered as #1, #2, and #3 in that order (the #2 is in the middle; the #3 is the last one the light passes through) along a line. They are all the same (usually the polarizers #2 and #3 are also called analyzers). The angle between the transmission axes of the polarizers #1 and #2 is 30 degrees, while the angle between the transmission axes of the polarizers #2 and #3 is 90 degrees. What percentage of the unpolarized light gets through the polarizer #3?

Explanation / Answer

If Let I0 is the intensity of light that incidents on the second polarizer (2). Since the angle between polarizers 1 and 2 is 300 then the intensity of transmitted light can be obtained using Malus Law. I2 = I0 cos2 30 = I0 (0.75) Now this light incidents on the third polarizer. The angle between second and third polarizers is 900. Hence the intensity of light is I3 = I2 cos2 90 = I3 (0) = 0. That means no light is passed through the third polarizer. Because the angle between second and third polarizers is 900. Hence the light which is transmitted through second polarizer suffers total internal reflection at the third polarizer. [Malus Law: ---- If the angle between the polarizer and analyzer is ?, then the intensity of light transmitted through analyzer is It = I0 cos2 ?, Here I0 is the light intensity that falls on analyzer.]

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