What Is the Prism Made Of Given Its Apex Angle and Minimum Deviation?

[skull]

Ok so here's a homework question. I honestly don't know where to begin.

A prism with an apex angle of 40 degrees induces a minimum deviation of 20 degrees. What is the prism made of.

Judging by what the question is asking for, I think I need to find the refractive index thru Snells law, but i don't know where to start.

All help is appreciated.

 

[berkeman]

Can you sketch how the light goes through the prism? Start with a single ray incident on one side (is the incident angle given or understood somehow?), and sketch what it does as it enters the prism glass, then it goes straight to the other face, where it bends again as it goes back into the air. The bend that happens at each of the two faces is governed by Snell's law as you say. So draw the sketch and write the two Snell's law equations.

Then for "minimum deviation", do they mean the angle of the red light ray that is still visible (red is deflected less by a prism -- just remember that red is on the outside of rainbows ROYGBIV).

 

[Doc Al]

The "angle of deviation" of light through a prism depends on the angle of incidence with the prism surface. The minimum angle of deviation is a characteristic of a prism that depends on its apex angle and index of refraction. The formula for minimum deviation is probably in your book. (Good luck if you have to derive it.) It turns out that the minimum deviation occurs when the refracted beam travels parallel to the side opposite to the apex angle (the path is symmetric).