Fermat's principle and Variation principle

Fermat's principle

The minimum "action" path is found by the Monte Carlo method. Here, the "action" is the time required for light to go from (0,0) to (1,1). The refractive index is set to smaller values for larger x. The curve is the solution to the Euler equation when n(x,y)=1/(x+1).

Calculation of light path

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