I have a short length of 10mm Perspex rob that I used to make the optical rob from. It worked well but the focus is completely out. I used a 13 mm radius in my attempt, which is the same as the original one I purchased; however, my viewing rod is shorter and would require a different radius to focus correctly.

I was wondering if anyone knows the formula to calculate the focal length so that I cut the curved end to create a focal point at exactly the other end of the rod, where I have the cross hairs marked? I spent a few hours online but can’t seem to find this equation.

The refractive index of the Perspex should be about 1.495.

I tried another optical rod with radius 11 and it was much better.

They are quite time intensive to make so I do not want to have to make many at different radii to try find the correct length, also I am running out of Perspex rod. I live in a remote area so driving to buy more Perspex rod is a 200km round trip.

If anyone has any knowledge in this area, I would appreciate your help.