Focal length of a sphere with refractive index gradient

[mypony4eva]

Homework Statement

We take a sphere (1mm) which has a parabolically changing refractive index, which is given in a function.

Homework Equations

Depending on the gradient of the refractive in the sphere, how does it correlates with the focal length.

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.

 

[dauto]

You said " refractive index, which is given in a function". What function is that? Please provide all the information in the problem.