I have been asked to write down the taylor expansion for two concentric spherical surfaces with radii r1 and r2 of a lens and mirror combination which I think is called a Mangin Mirror.

It is supposed to be related to the x and y axis positions.

Also, I have been asked to derive the optical path length of the incident light being reflected back the surface of the lens with radius r1.

I don't know were to start for either question.

Any ideas would be much appreciated!!