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.
Manus's Law: I = Imax cos2 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= Imax cos2 θ = Imax cos2 ωt
I= Imax/2 (1+ cos(2ωt))
Then the light from the second polarizer is:
I= Imax/2 (1+ cos(2ωt)) cos2 (90-ωt)= Imax/2 (1+ cos(2ωt)) sin2 (ωt)
and this turns into:
Imax/4 (1+ cos(2ωt))(1- cos(2ωt))
Imax/4 (1- cos2 (2ωt))
And for the answer we have:
Imax/8 (1- cos(4ωt))
The problem is the book expects the solution to be:
Imax/16 (1- cos(4ωt))
So I am off by a factor of 2. Can anyone see my problem or could it be a typo?