Starting from the Euler-Lagrange equations, show that the condition for the variation of the integral to be stationary is
In a medium with speed of light the ray path taken by a light signal between two points satisfies the condition that the time taken is stationary. Consider the region and suppose . Derive the equation for the light ray path . Obtain the solution of this equation and show that the light ray between and is given by
Sketch the path for close to and evaluate the time taken for a light signal between these points.
[The substitution , for some constant , should prove useful in solving the differential equation.]