Question

In the lectures, we found an expression for the refractive index of a metal at high frequencies. Starting from this result for n(ω), derive expressions for the phase velocity VP(ω) and group velocity vG(ω) of waves in a metal at frequencies above the plasma frequency. What is the value of the product of the group velocity and the phase velocity? In this problem, we are not concerned with frequencies below the plasma frequency, because metals are opaque for ω<ωp.

Answer 1

The phase velocity and group velocity of waves in a metal at frequencies above the plasma frequency can be derived from the expression for the refractive index. The phase velocity is given by c/n(ω), where c is the speed of light in a vacuum. The group velocity is given by c/[1 + ω(dn/dω)], where dn/dω is the change in refractive index with respect to frequency.

Step-by-step explanation:

Starting from the expression for the refractive index of a metal at high frequencies, we can derive expressions for the phase velocity VP(ω) and group velocity vG(ω) of waves in a metal at frequencies above the plasma frequency. The phase velocity VP(ω) is given by VP(ω) = c/n(ω), where c is the speed of light in a vacuum. The group velocity vG(ω) is given by vG(ω) = c/[1 + ω(dn/dω)], where dn/dω is the change in refractive index with respect to frequency. The product of the group velocity and the phase velocity is given by VP(ω) * vG(ω) = c, which is the speed of light in a vacuum.