1. The problem statement, all variables and given/known data Linearly polarized light of wavelength 5890 A is incident normally on a birefringent crystal that has its optic axis parallel to the face of the crystal, along the x axis. If the incident light is polarized at an angle of 45° to the x and y axes, what is the probability that the photons exiting a crystal of thickness 100.0 microns will be right-circularly polarized? The index of refraction for light of this wavelength polarized along y (perpendicular to the optic axis) is 1.66 and the index of refraction for light polarized along x (parallel to the optic axis is 1.49. 2. Relevant equations I know that |x'> = cosΦ|x> + sinΦ|y> and that |y'>= -sinΦ|x> + cosΦ|y>. I also know that the right-polarized state is given by |R> = 1/√2 |x> + i/√2 |y>. 3. The attempt at a solution When the light first enters, it is in the state |x'> = 1/√2|x> + 1/√2|y>. So, when it is refracted, it has a new angle with respect to the x axis. This new angle given by Snell's Law is, sinα = √2 / 1.49. So, the particle's state with respect to x is |x''> = cosα|x> + sinα|y>. The probability of this happening is |<x''|x'>|2 which is (cosα/√2 + sinα/√2)2 ~.7988. Since its a birefringent crystal, some particles have also been scattered with respect to the y axis, where its angle is given by sinβ = √2 / 1.66. So, these particles' state with respect to y is |y''> -sinβ|x> + cosβ|y>. The probability of this happening is |<y''|y'>|2 which is (-sinβ/√2 + cosβ/√2)2 ~0.054. When it reaches the other side of the crystal, the probability that it exits in the state |R> is given by |<R|x''>|2. This gives ( (cosα)/√2 + (i sinα)/√2 )*( (cosα)/√2 - (i sinα/√2 ) = ½. For the other stream that was in the |y''> state, the probability it exits in the state |R> is given by |<R|y''>|2. This gives ( (-sinβ)/√2 + (i cosβ)/√2 )*( (-sinβ)/√2 - (i cosβ)/√2 ) = ½. The total probability then becomes the first probability of going into the x'' state multiplied by the probability of going from the x'' state to the R state, which is ~ (.7988)*.5 = .3994 added to the probability of going into the y'' state multiplied by the probability of going from the y'' state to the R state, which is ~ (.054)*.5 = .027. The sum of these probabilities is ~ 0.4267 or roughly 43%. However, when I checked the answer at the back of the book, it said 0.12 or 12%. I didn't use the thickness of the crystal or the wavelength of the light, but I'm not sure whether they are required in solving the problem. Any help would be appreciated. Thanks.