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Optics in Lobachevsky geometry

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    l = ∫n dl

    3. 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...
  2. jcsd
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