Chapter 9.8, Problem 18MP

In Problems 11 to 18, use Fermat’s principle to find the path of a light ray through a medium of index of refraction proportional to the given function.

${(x+y)}^{1/2}$ Hint: Make the change of variables ( ${45}^{°}$ rotation). $X=\frac{1}{\sqrt{2}}(x+y),Y=\frac{1}{\sqrt{2}}(x-y);\text{ what is }d{X}^2+d{Y}^2?$