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.

**Part A**

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*.

*θ=*

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