Wavelength-dependence of refractive index in internal reflection spectroscopy?
Yes it should, but it doesn't matter much.

In physics, roughly speaking, everything depends on everything. We wouldn't be able to do a thing if we couldn't tell what is important and what isn't. Now let's see how much the refractive index actually changes as $\lambda$ goes, say, from 400 to 800nm (thus covering the entire visible range).



(source)

Looks like $n$ of a heavy flint glass goes from 1.85 to 1.75 (that's a change of 5%, in most other materials even less), while $\lambda$ changes by... how many percent?