I Group velocity for an electromagnetic wave inside glass

AI Thread Summary
The group velocity of an electromagnetic wave in glass can be calculated using the formula v_g = v_p + k(d v_p/dk). Given that v_p = c/n, it can be expressed as v_g = c/n + k(-ω/k^2) with k defined as ωn/c. The discussion highlights the importance of considering dispersion, where ω is a function of k, necessitating the inclusion of dω/dk in the derivative for accurate calculations. The mention of k_0 instead of k raises questions about their differences, which are not fully explored in the thread. Understanding these concepts is crucial for accurately determining wave behavior in dispersive media.
happyparticle
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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
 
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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.
 
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