A beam of initially unpolarized light (intensity I_0) is sent through polarizer

Question

A beam of initially unpolarized light (intensity I_0) is sent through polarizer A, and the intensity of the plane-polarized light that emerges is I_A. The polarized light I_A then passes through a second polarizer B, which can be rotated so that its polarization axis forms an angle between 0 degrees and 90 degress to the axis of polarizer A. The intensity of the light that emerges from polarizer B is I_B.

a. What is (I_A)/(I_B) [The fraction of I_0 that is transmitted through polarizer A]?

b. If I_B has 80.0% of the intensity of I_A, what is the angle between the axes of two polarizers?

c. If I_B has only 30.0% of the intensity of I_A, what is the angle between the axes of two polarizers?

Explanation / Answer

Part A)

The first polarization is 50% (or .5) since half of the unpolarized light intensity goes through the first polarizer

Part B)
Apply I = Iocos^2(angle)

.8 = cos^2(angle)

angle = 26.6 degrees

Part C)

Apply I = Iocos^2(angle)

.3 = cos^2(angle)

angle = 56.8 degrees

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