Sine laws of spherical singlets

[difalcojr]

There is free OSLO EDU raytracing software which is limited up to 10 surfaces for free educational version.

Should only need two surfaces, thankfully.
Trace a planar ray through the planar model with the values shown in the last post's diagram, and trace any diverging or converging ray angle through it too. See if the input and output ray angles will be the same.
I have my doubts still on existing software being able to do thick lens, trigonometric tracing, as this requires.

 

[difalcojr]

You may find this treatment interesting (shaping aspheric second surface) .
https://royalsocietypublishing.org/doi/epdf/10.1098/rspa.2014.0608

From what I can tell the family of aspheric model lenses free from all orders of spherical aberration as shown in the article, is akin to this family of spherical model lenses free from all orders of spherical aberration.
A modern, aspheric singlet and a classic, spherical singlet. Both with zero SA. They could be paired together, possibly.
The spherical model here is exceedingly simple, while the modern physics aspheric model is the opposite. From a geometrical optics point of view, the aspheric model seems similar to Descartes' ovals.
The family photo of spherical models is shown in that large array in a previous post here. If you turn those pictures sideways, you will see how highly groomed their "haircuts" are. An ordered universe.

 

[berkeman]

It turns out that the OP is trying to use PF for peer-review of his work, so this thread is closed per the PF rules.