- #1
raopeng
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Homework Statement
In the upper half of a (x,y) plane endowed with a refractive index of n(y) = 1/y, find the form of light ray.
Homework Equations
l = ∫n dl
The Attempt at a Solution
My method is to construct a functional for optical path, obtaining the result using Euler-Lagrangian equation which would give the desired result of circle with arbitrary radius(the geodesic of the Poincare model). However as I find this question in Arnold's ODE, is it possible to start from a more "ODE" prospective, because I believe Arnold didn't expect the use of Hamilton's principle from this question...