The paint used on highway signs often contains small transparent spheres which provide nighttime illumination of the sign's lettering by retro-reflecting vehicle headlight beams. Consider a light ray from air incident on one such sphere of radius r and index of refraction n. Let theta be its incident angle, and let the ray follow a path such that the ray exits the sphere in the direction exactly antiparallel to its incoming direction. Considering only rays for which sin(theta) can be approximated as theta, determine the required value for n.