# How to estimate the index of refraction of a material based upon its chemical composition

I want to be able to estimate what the index of refraction of a material is based upon the chemical makeup of the material. For example what equation would I use to estimate the index of refraction of a material that is 70% Germanium and 30% Diamond?

I found the equation $$n^2 = n_0^2 + m/m1 * (n_1^2-n_0^2)$$ from the link: https://optiwave.com/optifiber-manuals/optical-fiber-refractive-index-of-fibers/ but that doesn't explain what the value m is. Is it a typo? My guess is that they meant to type $m_0$ not $m$ but I'm not sure. Is this equation even correct? I can't find it anywhere else and it didn't list a name or law relating to it.

This equation is simply describing an interpolation, based on the ratio of the number of atoms. For your example, this formula would estimate the refractive index to be $\sqrt{0.7n_{\rm Ge}^2+0.3n_{\rm C}^2}$.

But of course, this formula would be wrong. It is an approximation that is only appropriate for very small amounts of added dopants into the host material. You'll see from the website that they are concerned with engineering variations in the refractive index on the order of $<0.01$.

• I think you mean $\sqrt{.7n_{\rm Ge}^2+.3n_{\rm C}^2}$?
– Chris
Nov 2, 2017 at 5:16