Two polarizing sheets have their transmission axes crossed so that no light is t

Question

Two polarizing sheets have their transmission axes crossed so that no light is transmitted. A third sheet is inserted so that its transmission axis makes an angle theta with the transmission axis of the first sheet. Unpolarized light of intensity I_0 is incident on the first sheet. If the middle polarizing sheet is rotating at an angular speed co about an axis parallel with the light beam, find an expression for the intensity transmitted through all three sheets as a function of time. Assume that theta = 0 degree at time t = 0. (Use the following as necessary: I_0, omega, and t. Express angles in radians.)

Explanation / Answer

I1 = Io/2

at any time t , the second polarizer is at angle theta = wt

I2 = I1*(coswt)^2

3rd polarizer is angle theta = 90 - wt

I3 = I2*(cos(90-wt)^2)

I3 = I2*(sinwt)^2

I3 = I1*(coswt)^2 * (sinwt)^2

I3 = Io/2 *(coswt)^2 * (sinwt)^2

I3 = Io/4*(sin2wt)^2

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