How Does Light Behave When Passing Through a Birefringent Prism?

[Xyius]

My big problem here is with the geometry...

Homework Statement

I just took a picture of the problem. It's 15-10.
http://img839.imageshack.us/img839/9712/optics.jpg

Homework Equations

$$n_1sin\theta_1=n_2sin\theta_2$$
$$n_{\bot}=1.6584$$
$$n_{Parallel}=1.4864$$ (I can't find the Parallel sign)

The Attempt at a Solution

So the prism is a birefringent material. The beam of light which oscillates in and out of the page is perpendicular to the optical axis and is going into a medium in which it will be parallel, so to find the angle of refraction..
[tex]1.6584sin(45°)=1.4864sin\theta_{r1}
This gives an angle of refraction of 52.1°. Doing the opposite with the other beam of light gives an angle of 39.33°.

So for the first part, their angle of deviation is about 13°. The problem is, I cannot determine the angles in which the beams hit the other wall of the prism. Every time I think I get it, the bottom angle has an angle greater than its critical angle so total internal reflection would happen. This isn't the case from the picture so I must be doing something wrong. How would I get the angles in which the light hits the walls?

Thanks!

 

[Delphi51]

Like this? I worked my way around the triangle from the beam entry to its exit from the prism.