1. The problem statement, all variables and given/known data We take a sphere (1mm) which has a parabolically changing refractive index, which is given in a function. 2. Relevant equations Depending on the gradient of the refractive in the sphere, how does it correlates with the focal length. 3. The attempt at a solution I know I saw somewhere an analytic solution (or at least an analytically derived approximation) formula somewhere, but I don't have a clue where to find it.