Refraction from higher to lower density can lead to a peculiar phenomenon. Instead of exiting into the lower density, the light can be internally reflected and "trapped." In the language of Snell's Law, certain angles in the higher density material will have a 90? refraction angle.

Such a critical angle ? is shown above in a picture of an optical fiber. The fiber is composed of a core and a covering with indices of refraction given by n₁ = 1.465 and n₂ = 1.45. Light enters the core at an angle ? and refracts an angle ?. Then, it meets the covering at a critical angle. Find an expression for the incoming angle ? as a function of only n₁ and n₂.

Refraction from higher to lower density can lead to a peculiar phenomenon. Instead of exiting into the lower density, the light can be internally reflected and "trapped." In the language of Snell's Law, certain angles in the higher density material will have a 90" refraction angle. Such a critical angle y is shown above in a picture of an optical fiber. The fiber is composed of a core and a covering with indices of refraction given by m = 1.165 and ny = 1.15. Light enters the core at an angle o and refracts an angle S. Then, it meets the covering at a critical angle. Find an expression for the incoming angle a as a function of only n, and ng. Hints: cos / = sin y and sin' 8 + cos 8 = 1