3 Photons going through 3 Polarizers

[JoshWard]

Homework Statement

Suppose we set up a sequence of three polarizers with orientations 45 degrees, 75 degrees and 45 degrees, where the angles refer to how much each polarizer is rotated relative to the vertical direction.

If we send three vertically (i.e. 0 degrees) polarized photons in either 0, 1, 2, or 3 photons might pass through all the polarizers. What is the probability for each of these possibilities?

Homework Equations

lθ> = cos(θ)l0 degrees> + sin(θ)l90 degrees> (Dirac Notation)
Probability = cos^2(θ)

The Attempt at a Solution

Well what I have is that when the photons go through the first polarizer, the probability of 1 getting through is 50%, 25% for 2 and so on. Then the photons become polarized at 45 degrees. I'm just having a hard time figuring out how to continue through the 75 degrees polarizer and the last 45 degree polarizer. All I want to know is how to set up the photons going through the 75 degree polarizer, from there I can get the rest.

 

[vela]

When you say the probability is equal to $\cos^2 \theta$, what exactly does $\theta$ represent? If you understand that, how to deal with the second polarizer is straightforward.