In a certain medium the relationship between the group and phase velocities of an electromagnetic wave has the form `uv = c^(2)`, where `c` is the velocity of light in vaccume. Find the dependence of permittivity of that medium on wave frequency, `epsilon(omega)`.

Explanation

We have
`uv = (omega)/(k)(d omega)/(dk) = c^(2)`
Intergrating we find
`omega^(2) = A+c^(2) k^(2), A` is a constant.
so `k = sqrt(omega^(2) - A)/(c )`
and `v = (omega)/(k) = (c )/(sqrt(1- (A)/(omega^(2))))`
writing this as `c//sqrt(epsilon(omega))` we get `epsilon(omega) =1-(A)/(omega^(2))`
`(A` can be `+ve` or negative)