Undergrad Group velocity for an electromagnetic wave inside glass

[happyparticle]

Hi,

I saw that the group velocity for an electromagnetic wave can be calculate with the following formula
$v_g = v_p + k \frac{d v_p}{dk}$

Thus, since $v_p = \frac{c}{n} = \frac{\omega}{k}$

Is it correct to say that $v_g = \frac{c}{n} + k(- \frac{\omega}{k^2})$ where $k = \frac{\omega n}{c}$ and $\omega = \frac{2 \pi v_p}{\lambda}$

Moreover, I see sometime $k_0$ instead of k. I'm wondering why and what's the difference.

Thanks

 

[nasu]

If there is dispersion (when the group and phase velocities are different) omega is a function of k. So you need to include $$d\omega/dk$$ to your derivative.