He felt that although his glass-making experiments were not going well, eventually he would be able to produce some glass of acceptable quality. Then he would grind them into lenses and make microscopes and telescopes.
Yet he had completely forgotten the principles of optics.
He also forgot the exact shapes of convex mirrors and concave mirrors and how they affected the optical path.
So he wanted to calculate them.
However, he hadn't studied optics seriously; he crammed before the tests and passed, forgetting everything afterward.
He didn't plan to make highly standard microscopes or telescopes.
A microscope that could see bacteria and an astronomical telescope that could see the surface of the moon and nearby stars would satisfy his requirements.
Galileo lived even before Newton, and he could already grind lenses to observe bacteria and the surface features of some closer celestial bodies.
Logically, the difficulty of this shouldn't be too high.
