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ceran
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Homework Statement
S solid uniform glass sphere is surrounded by air. The sphere has radius R and refractive index n. As shown in the picture, a light ray traveling in air, parallel to a diameter of the sphere, enters the sphere, reflects off the far side, then exits the sphere traveling in a direction exactly opposite to its original direction.
Showing all details of your solution, find the relationship that expresses x (for 0<x<R) in terms of n and R in the situation shown in the picture.
Homework Equations
Snell's Law, nasin(thetaa) = nbsin(thetab)
The Attempt at a Solution
I labelled the angle of incidence and angle of refraction as a and b in the diagram.
Since n for air is one, the equation should become
sin(a) = nbsin(b)
Due to geometry, sin(a) will be equal to x/R. However, I cannot figure out an expression for sin(b) in terms of x, R, and n. I have tried for a long time, and just cannot figure out the geometry of the problem. Thanks for your help.