Problem 5.62

A ray of light propagating in an isotropic medium with refractive index $n$ varying gradually from point to point has a curvature radius $\rho$ determined by the formula $$\frac{1}{\rho}=\frac{\partial}{\partial N}(\ln n)$$ where the derivative is taken with respect to the principal normal to the ray. Derive this formula, assuming that in such a medium the law of refraction $n \sin \theta=$ const holds. Here $\theta$ is the angle between the ray and the direction of the vector $\boldsymbol{\nabla} n$ at a given point.