I read this from a lecture note(attached) of Geometric Optics. It's said that the eikonal equation for light rays [itex]\frac{d}{ds}(n(\vec{r})\frac{d\vec{r}}{ds})=\frac{\partial n}{\partial \vec{r}}[/itex] is analogous to Newton's Law, however it doesn't tell which Newton's Law is referred to. (In the equation, [itex]\vec{r}[/itex] is position vector, [itex]s[/itex] is the raw path length, [itex]n[/itex] is the refractive index).(adsbygoogle = window.adsbygoogle || []).push({});

The equation can be rewritten to [itex]\frac{d^2\vec{r}}{d\sigma^2}=\frac{1}{2}\frac{\partial n^2}{\partial \vec{r}}[/itex] where [itex]d\sigma=n^{-1}ds[/itex]. 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.

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

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