## calculate the appropriate dimensions for a magnifier and thin prism working together

Hi! :)

I'm trying to calculate the appropriate lenses to use for a project. I need to magnify a 50mm by 50mm square image that is 40mm from a magnifying lens (with a radius of 12.5mm). Due to size constraints, I also have a thin prism to redirect the light. Assume the viewer (an eye) is within a centimeter from the lens on the opposite side of the thin prism. Additionally, the lenses are centered vertically. An image is attached displaying the configuration on how it is supposed to be arranged.

Questions:

1. What are the appropriate specs (magnification, focal length, etc.) for the magnifying lens to capture the entire 50x50 image, however magnify it as much as possible?

2. What angle should the thin prism be to focus approx 7mm from the current path?

3. What (if any) considerations should be taken into mind when the viewer is an eye? On the equations I've seen, they don't seem to ever talk about a person viewing through the magnifier.

4. What is the process used to calculate both the magnifying lens and thin prism?