Electromagnetic radiation (known as Cerenkov radiation) is emitted when a charged particle moves through a medium faster then the local speed of light. It should be stressed that the particle is never going faster then the speed of light in vacuum (or c), just faster than the speed of light in the material (which is always less than c).
When a charged particle passes straight through a medium faster than the local speed of light, it will emit Cerenkov radiation in a cone. Let's see how the cone angle is correlated to the speed of the particle.
If a particle is traveling straight through a material with index of refraction n at a speed v, what is the angle θ between the vector of the propagating Cerenkov radiation and the vector in the direction of the propagating particle?
Express your answer in terms of v, c, and n.