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dingo_d

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## Homework Statement

Electromagnetic wave, with the frequency [itex]\omega[/itex], travels through the medium for which:

[itex]\epsilon=\epsilon_0\left(1+\frac{\omega_p^2}{\omega_0^2-\omega^2}\right)[/itex]

where [itex]\omega_p[/itex] and [itex]\omega_0[/itex] are constants. How does the expression for the group velocity [itex]v_g(\omega)[/itex] looks like? What condition do the constants need to satisfy so that the relativity principle [itex]v_g\leq c[/itex] should hold?

## Homework Equations

The expression for group velocity of the traveling wave is [itex]v_g=\frac{d\omega}{dk}[/itex]

where [itex]\omega[/itex] is angular frequency and k is wave number (vector in 3D).

## The Attempt at a Solution

The problem is I don't really know where to start. I have the expression for electric permittivity, and I don't know how to connect that with group velocity of the emw. Does anyone know how to start, and what to look? Thnx!