# Focal length of a sphere with refractive index gradient

1. Jun 16, 2014

### mypony4eva

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.

2. Jun 17, 2014

### dauto

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