# 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.

http://ift.tt/1vvjICF