Model a parabolic GRIN fiber by the equivalent multiple-step approximation.

Let n1=1.5, Δ=0.01. Divide the radius into 10 equal parts. Consider a ray crossing the fiber axis at 5° with respect to that axis (and inside the fiber). Sketch its progress through the fiber until it turns back and re-crosses the fiber axis. (The angles can be magnified on your sketch.)

At what value of r/a did the ray turn back by total reflection?