# How is Eikonal Equation analogous to Newton's Law?

by genxium
Tags: analogous, eikonal, equation, newton
I read this from a lecture note(attached) of Geometric Optics. It's said that the eikonal equation for light rays $\frac{d}{ds}(n(\vec{r})\frac{d\vec{r}}{ds})=\frac{\partial n}{\partial \vec{r}}$ is analogous to Newton's Law, however it doesn't tell which Newton's Law is referred to. (In the equation, $\vec{r}$ is position vector, $s$ is the raw path length, $n$ is the refractive index).
The equation can be rewritten to $\frac{d^2\vec{r}}{d\sigma^2}=\frac{1}{2}\frac{\partial n^2}{\partial \vec{r}}$ where $d\sigma=n^{-1}ds$. It's actually the rewritten equation that is said to be analogous to Newton's Law, but I have no idea how to interpret it.