= State Fermat's principle governing the paths traced by light rays in a medium. A horizontally stratified medium has refractive index μ(z) Va- bz, where z is height and a and b are positive constants. Prove that the path of a light ray within a vertical plane in this medium is an inverted parabola. Show further that all such parabolas have their directrix in the plane z = a/b. [The directrix of a parabola in the standard form y2 = 4ax is the line x = -a.]

= State Fermat's principle governing the paths traced by light rays in a medium. A horizontally stratified medium has refractive index μ(z) Va- bz, where z is height and a and b are positive constants. Prove that the path of a light ray within a vertical plane in this medium is an inverted parabola. Show further that all such parabolas have their directrix in the plane z = a/b. [The directrix of a parabola in the standard form y2 = 4ax is the line x = -a.]