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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} (90ωt)= 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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