Light travels in the vertical x z-plane through a slab of material which lies between the planes z=z_0 and z=2 z_0, and in which the speed of light v(z)=c_0 z / z_0. Using the alternative formulation of Fermat's principle, given in the previous question, show that the ray paths are arcs of circles. Deduce that, if a ray enters the material at left(0, z_0 right) at an angle to the vertical, pi / 2-θ, of more than 30ᵒ, then it does not reach the far side of the slab.