A common trick in fiber optics is to send several colors of light down the same fiber (this is a form of what's called multiplexing). Each color of light can carry a separate signal, letting you squeeze more information into your beam. This, of course, leaves you with the problem of how to separate the colors back out once your beam gets to where its going. One way to do this involves total internal reflection. The index of refraction of glass isn't fixed; it's actually a function of frequency. Specifically, the index of the glass n and the angular frequency ω of the light are related by the equation below. Since different colors of light see different indices of refraction, different colors of light will see different critical angles. Suppose we have a beam with green light (frequency ω=3.7e+15 rad/s and red light (frequency ω=2.9e+15 rad/s traveling through this glass. Eventually, it's going to hit a glass-air boundary. At what angle of incidence θ should the light hit the boundary if we want the green light to stay in the glass and the red light to leave? Choose the smallest angle of incidence that works, and enter it in degrees (unit "deg").

A common trick in fiber optics is to send several colors of light down the same fiber (this is a form of what's called multiplexing). Each color of light can carry a separate signal, letting you squeeze more information into your beam. This, of course, leaves you with the problem of how to separate the colors back out once your beam gets to where its going. One way to do this involves total internal reflection. The index of refraction of glass isn't fixed; it's actually a function of frequency. Specifically, the index of the glass n and the angular frequency ω of the light are related by the equation below. Since different colors of light see different indices of refraction, different colors of light will see different critical angles. Suppose we have a beam with green light (frequency ω=3.7e+15 rad/s and red light (frequency ω=2.9e+15 rad/s traveling through this glass. Eventually, it's going to hit a glass-air boundary. At what angle of incidence θ should the light hit the boundary if we want the green light to stay in the glass and the red light to leave? Choose the smallest angle of incidence that works, and enter it in degrees (unit "deg").