I'm making a magnifying glass from scratch. What's the mathematically ideal shape?
As the ultimate test of my lapidary skill, I've decided to make a functional aspheric magnifying glass.
Instead of the typical spherical convex lens faces, I'd like to try for something mathematically pleasing. I'm reading that the ideal lens (one which focuses parallel light to a "perfect" focal point) will have one face elliptical and one hyperbolic--is this correct? And if so, what ellipse and hyperbola would work for me in this case?
I plan to 3D print the inverted surfaces and use those as an indicator of where I need to take off more material. The end result will not be perfect, but I'm okay with that. Any help/guidance is much appreciated!