I would also be interested in any collections of formulas (with explanations of their uses) for these purposes. I have found some, but not enough to do these calculations on my own.
jOcular (java8, jar file, pre-alpha but gets a couple of good reviews) https://sourceforge.net/projects/jocular/Optical Design Software for optical systems comprised of light sources, lenses, apertures, prisms, imagers, photometers, etc. Simulate light through the system and compute images and intensities at various locations in the design. Has a help page https://sourceforge.net/p/jocular/wiki/jOcular%20Help/ Has a wiki page with optical and technical stuff: https://sourceforge.net/p/jocular/wiki/Technical%20and%20The...
VOpR - a virtual optical rail(java, Alpha) https://sourceforge.net/projects/vopr/ VOpR allows to create and evaluate simple optical systems, in which the basic optical elements are arranged along the optical axis. The current supported optical elements are: spaces, spherical lenses, circular apertures and flat blocks of some optical medium. No reviews
LaserCalc https://sourceforge.net/projects/lasercalc/ LaserCalc is an Open Source wxWidgets application for the calculation of optical beam paths and laser resonators based on Gaussian beam matrix optics. In addition beam paths can be optimized to match given beam parameters (mode matching). 3 good reviews.
OpenRayTrace https://openraytrace.sourceforge.net OpenRayTrace is the cross platform optical design software. It uses Python, wxPython, pyOpenGL and related APIs.
It has the following features: Skew Ray Tracing Spot Diagrams Random Ray Tracing for extended Sources Aberration Plotting pre-alpha, no reviews, docs seem to be missing. Pretty pictures, though.
Some basic info: https://www.pencilofrays.com/lens-design-forms/ https://www.opticaldesignsoftware.net