Wavelength-dependence of refractive index in internal reflection spectroscopy? In many literature sources (web example), only a single value for the refractive index is assumed for the infrared element, and another is typically assumed for the sample substance. However, should not the refractive index be wavelength-dependent? So the wavelength-dependence of the penetration depth,

\begin{equation}
d_p = \frac{\lambda}{2\pi n_1 \sqrt{\sin^2\theta - (n_2/n_1)^2}}
\end{equation}

would not only be in the numerator, but also in the denominator: $n_1 = n_1(\lambda)$ and $n_2 = n_2(\lambda)$? Here $d_p$ is the penetration depth, $\lambda$ is wavelength, $\theta$ is the incident angle, and $n_1$ and $n_2$ are the refractive indices of the infrared element and sample, respectively.
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?