(I'm not entirely sure whether this should go here on on the Physics stack exchange. Tell me if I'm wrong :))
To my understanding a lens can be made by intersecting two spheres. This causes spherical abberation though, and a better aspheric lens can be made which focuses the light into one exact point.
How could I describe the shape of a lens as a function $ f(x) = y $ where $x$ is the distance from the center of the lens and $y$ is the thickness of the lens at that point. (To clarify, an equation like $ f(x) = \frac{1}{20}x^2 + 2, -6 < x < 6$ is roughly like what I am looking for).
Specifically, I'm looking for a function to describe a convex lens, and in particular the "normal" kind - i.e. the typical one you would learn about in Physics where photons converge to a single point.