What's the type of the ideal shape of a surface of a plano-convex lens to focus a parallel beam at the point? Considering the lens turned its flat side to a beam.
Surely it must be aspheric: probably hyperbolic or parabolic - but i have no idea how to figure it out.
The formula of a refraction at spherical surfaces is not that easy but possible to get. But how to deal with hyperbolic or parabolic surfaces?
Or is there a simpler way to answer my question?