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Minimum Deviation Angle

by JSGandora
Tags: deviation, minimum, optics, prism, snell's law
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JSGandora
#1
Nov3-11, 07:31 PM
P: 92
1. The problem statement, all variables and given/known data
The apex angle of a prism is [itex]50.0^\circ[/itex] and the index of refraction of the prism material is [itex]1.66[/itex]. What is the minimum deviation angle?



2. Relevant equations
Snell's Law: [itex]n_1\sin(\theta_1)=n_2\sin(\theta_2)[/itex]


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

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