I've been studying in optics the macroscopic maxwell's equations, and how electromagnetic fields propagate through different mediums. Over there, the index of refraction appears, as a complex function that generally depends on $\omega$, with both refraction and absorption terms: $n_c=n+i\kappa$.
I understand how this affects the speed at which light propagates, both macro and microscopically, and how this affects to how light is absorbed when it transmits through the medium, but I don't get yet how this index changes the direction of light, producing dispersion. I mean, all time I'm seeing those effects as something that separates dispersive from non dispersive mediums and all that stuff, and I don't know how light is actually dispersed. As it's something that happens when changing medium, I guess it's an interface effect, and we haven't seen those effects yet, but I would like to know an explanation.