A spherical lens - where is a focus? Is it a point, or we must have not spherical surfaces for a point?
One problem for Mathcad!
A spherical lens doesn't focus to a point (hence the term "spherical aberration"). The formula you show is a thin lens approximation. It's good for high F# lenses (long focal length compared to diameter), not so good for low F# lenses. This form is better, where d is the center thickness:
For spherical surfaces there's a "best form" lens, which gives minimum spherical aberration. The shape factor for such a lens is
where s0 is the object distance (negative if to the left of the lens). The curvature (1/radius) of the surfaces are then:
With animation!
