Focal length of a sphere with ref. index gradient.

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.

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