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Application of the euler equations using fermats principle

  1. Oct 30, 2012 #1
    1. The problem statement, all variables and given/known data
    The speed of light in a medium with index of refraction n is c/n, where c is the speed of light in vacuum. Notice that n ≥1:
    Suppose a light ray travels in the xy-plane between (x1; y1) and (x2; y2) in a non-uniform
    material so that n(x) is the refractive index of the material at x.
    Show that the path of the ray is y(x) = y1 + ∫(x1 -> x) z/(sqrt(n^2(x') - z^2) dx' ,where z is a constant

    2. Relevant equations
    Euler's Equations



    3. The attempt at a solution

    I am aware you are suppose to split up the path into strips of thickness dx but am unaware of how to approach this. Solution would be very helpful. Thanks
     
  2. jcsd
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