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## Homework Statement

This is problem 71, chapter 38 in

*Physics for Scientists and Engineers 8th edition*by Serway/Jewett.

Three polarizers are situated in a straight line with one spinning in the middle with θ=ωt.

Find the intensity of light coming out the other side as a function of time.

The attachment is the diagram of the system.

## Homework Equations

Manus's Law: I = I

_{max}cos

^{2}θ. Where θ is the angle between the transmission axis for the two polarizers.

## The Attempt at a Solution

Through the first two polarizers we have:

I= I

_{max}cos

^{2}θ = I

_{max}cos

^{2}ωt

which becomes

I= I

_{max}/2 (1+ cos(2ωt))

Then the light from the second polarizer is:

I= I

_{max}/2 (1+ cos(2ωt)) cos

^{2}(90-ωt)= I

_{max}/2 (1+ cos(2ωt)) sin

^{2}(ωt)

and this turns into:

I

_{max}/4 (1+ cos(2ωt))(1- cos(2ωt))

I

_{max}/4 (1- cos

^{2}(2ωt))

I

_{max}/4 (1-(1+cos(4ωt)/2))

And for the answer we have:

I

_{max}/8 (1- cos(4ωt))

The problem is the book expects the solution to be:

I

_{max}/16 (1- cos(4ωt))

So I am off by a factor of 2. Can anyone see my problem or could it be a typo?

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