In this article we deduce the characteristic equation for trajectories performed by monocromatic light rays which propagate through medium with a variable refractive index. Although our deduction was inspired in techniques from variational calculus, it is presented in an elementar and self-contained way and it uses only basic concepts of differential and integral calculus. Besides deduction, we analyse certain general aspects of the equation and discuss some special cases also. In particular, we show that this equation leads to the Snell's Law for refraction of light as a limiting case.
Snell's law; Fermat's principle
