Determining refractive index at relativistic speeds

If you studied advanced physics at high school, there's a good chance that you remember Snell's law, which states how a ray of light bends when it crosses a boundary between two media. According to this law, the ratio of the sines of the incident and refracted angles is a non-universal constant, later understood as the relative refractive index of the refracting medium with respect to the incident one.