I had an idea to jerry-rig a handheld magnifying glass onto a computer projector, to convert the standard-throw lens into either a short-throw or a long-throw. But then I realized that I had no way to check it except to just try random things, hope they work, and be clueless why they don't.
I'm not looking for comprehensive math. More like:
A ray tracing diagram for every possible configuration of a single convex or concave lens or mirror, and an object on either side of the focal point for each. Maybe even on the "wrong" side of the element as well. Where is the image in each case, if there is one, and is it real (can be seen by putting a screen there) or virtual (can only be used as the object for another lens or mirror, which includes the one in our eyes)? I've seen a few of those, but everyone seems to copy or redraw the same 3 or so, which doesn't really help.
Given that, how to combine optical devices, using the image from one as the object for the next, without restricting the geometry to avoid overlapping the diagrams of single elements?
Again, I'm not looking for math, beyond what can be done with just mental notes and a 4-function calculator, but a good visual way to sanity-check a wacky idea. Not just the one above, which I suspect would be a challenge at best because of where the projector's image is, but in general.
