Simple Law of Refraction Problem

[opticaltempest]

Homework Statement

I am studying the Law of Refraction. I am at a point in my textbook called a "checkpoint". These are supposed to be simple questions to test understanding. I'm apparently not understanding thus far because I cannot figure out this problem.

http://img262.imageshack.us/img262/7029/refractionqn3.jpg

Homework Equations

Snell's Law?

The Attempt at a Solution

I'm sure the angles of line segments b and c (relative to a?) will be the determining factor. Since the problem says "original materials a" does that mean we measure all angles relative to line segment a? How do I proceed more mathematically on this problem - perhaps using Snell's law?

 

[Doc Al]

Definitely use Snell's law. Measure angles with respect to the normal, as usual with Snell's law.

 

[Moetasim]

I understand your confusion and am happy to help you with this problem. First, let's clarify a few things. The "original materials a" refers to the materials on the left side of the interface, while "original materials b" refers to the materials on the right side. This means that the angles of line segments b and c should be measured relative to their respective original materials, not line segment a.

Now, let's look at Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two materials. In this problem, we are given the index of refraction for each material, which is equal to the ratio of the velocity of light in a vacuum to the velocity of light in that material.

So, to solve this problem, we can use Snell's law and the given index of refraction values to calculate the angles of refraction for both materials. Remember to use the correct index of refraction for each material when calculating the angles. Once you have the angles of refraction, you can use the fact that the sum of the angles in a triangle is 180 degrees to solve for the missing angle.

I hope this helps you understand the problem better and gives you a starting point for solving it. Good luck!