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## Homework Statement

The conductivity of a plasma is defined as [itex]\sigma = i\frac{Ne^{2}}{m\omega}[/itex] where N is the electron density.

a) Prove the refractive index is: [itex]n = \sqrt{1- (\frac{\omega}{\omega_{p}})^{2}}[/itex] with [itex]\omega_{p} = \sqrt{\frac{Ne^{2}}{m\epsilon_{0}}}[/itex]

b) Show the Attenuation length is [itex]L = \frac{c}{\omega} \sqrt{\frac{1}{(\omega_{p}/\omega)^{2}-1}}[/itex]

## Homework Equations

[itex]k^{2} = \mu\epsilon\omega^{2} + i\mu\sigma\omega[/itex]

## The Attempt at a Solution

I can't find equations linking the refractive index to the dispersion relation. Also, don't know anything about the attenuation length.

Can I grab a push in the right direction?

Thanks

Edit: Right, for the first part, I stumbled upon the equation [itex]n^{2} = \frac{c^{2}}{\omega^{2}} k^{2}[/itex] but I get an answer inverse to the required answer, with an extra factor of [itex]c^{2}[/itex]. Can someone just verify I've almost got there or that that equation is completely wrong. Thanks.

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