# Speed of light and wavelength

Does the speed of Electromagnetic wave depend on its wave length? For vacuum I'm aware that it's a constant $$c=\frac{1}{\sqrt{\mu_o\epsilon_o}}$$. Similarly can we say speed of light in any medium is a constant and is equal to $$v=\frac{1}{\sqrt{\mu\epsilon}}$$.

If yes, then refraction shouldn't be possible right ?

If no, then does $$\frac{1}{\sqrt{\mu\epsilon}}$$ have any significance?

$$\epsilon$$ - and, to a lesser extent $$\mu$$ - depends on the frequency of the light. The atoms of the medium have a particular excitation frequency, or frequencies, and the polarisability of the atom rises as the EM frequency rises to a peak when it equals the atomic excitation frequency, and then falls off. It's standard forced SHM https://en.wikipedia.org/wiki/Harmonic_oscillator#Sinusoidal_driving_force . So different frequencies, and hence different wavelengths, have different velocities.
• does $v=\frac{1}{\sqrt{\mu\epsilon}}$ have any significance? – Vilvanesh Mar 22 at 16:23
$$n = \frac{c}{v}$$
(where $$c$$ is the speed of light in vacuum and $$v$$ is the speed in the medium) and the angle of refraction depends on $$n$$, the fact that light splits into colors when going through a prism tells us that $$n$$ depends on the wavelength, and then so does $$v$$.
• does $\frac{1}{\sqrt{\mu\epsilon}}$ have any significance? – Vilvanesh Mar 22 at 15:41