Up to now, we have obtained all of our results with the assumption that the medium was free from dispersion. This just meant that we assumed that the index of refraction was constant as a function of frequency, so all wavelengths were similarly affected. Of course none of our results so far depended particular strongly on this result, but in any event it is not correct. The permittivity (and to a lesser extent for transparent materials, the permeability) is a function of the frequency and thus the speed of light changes as a function of frequency as well for waves propagating in a dispersive medium.
By the way, when I say that it ``isn't correct'' I'm not asserting an opinion or mathematical conclusion. That's not how physics works. Rather it is always ultimately empirical: rainbows and prisms (not to mention opaque objects) remind us that most physical media are not free from dispersion. Understanding and modelling the dynamics of dispersion in a way that correctly explains these observed phenomena is a key step in the understanding of much modern physics, which involves the measurement and prediction of various susceptibilities (yet another way of writing the permittivity, basically, as you can see below) in both classical and quantum circumstances. A full understanding of the particular dispersion of a physical medium is possible only in the context of quantum theory, but to understand the phenomenon itself we can fortunately rely on a rather simple classical model that exhibits all the essential features observed in actual physical media.
