Axially Graded Plate. A plate of thickness d is oriented normal to the z axis. The refractive index n(z) is graded in the z direction. Show that a ray entering the plate from air at an incidence angle do in the y-z plane makes an angle O(z) at position z in the medium given by n(z) sin 0(z) = sin Go. Show that the ray emerges into air parallel to the original incident ray. Show that the ray position y(z) inside the plate obeys the differential equation (dy/dz)? = (n2/ sin20 - 1)-1