Homework Help: Minimum Deviation Angle

1. Nov 3, 2011

JSGandora

1. The problem statement, all variables and given/known data
The apex angle of a prism is $50.0^\circ$ and the index of refraction of the prism material is $1.66$. What is the minimum deviation angle?

2. Relevant equations
Snell's Law: $n_1\sin(\theta_1)=n_2\sin(\theta_2)$

3. The attempt at a solution
How would you approach this? I get a deviation angle of $50+\arcsin(1.66\sin(\theta))+\arcsin\left(\frac{ \sin(50-1.66 \sin(\theta))}{1.66}\right)$ using Snell's Law and angle chasing but I don't know how to minimize that. $\theta$ is the initial angle of incidence.

For some reason I think the solution should be much simpler than that. Can someone help me?