1.3-3 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 (2) at position z in the medium given by n(z) sin 0(z) = sin 00. Show that the ray emerges into air parallel to the original incident ray. Hint: You may use the results of Prob. 1.2-7. Show that the ray position y(z) inside the plate obeys the differential equation (dy/dz)? = (n3/ sin3 0 - 1)-1