Making a Concave Mirror Using 15th Century Technology (2018)
wp.optics.arizona.edu
wp.optics.arizona.edu
Does someone have a deeper explanation than this?
Between that, and the lathe, you can build the world.
then part of the time the edges are uncovered, while the centers are nearly always covered,
so the centers should grind faster. and both try to go concave,
this is however self-limiting: if the centers are ground slightly more than the edges, then the edges protrude and would grind faster again to catch up.
the used motions translating and rotating in 2 dimensions, result in spherical surfaces being the only solutions, concave and convex, flat and flat, and convex and concave.
its just that because of the initial phenomenon (the centers trying to grind faster than the edges, because the edges are unexposed part of the time) that you get spontaneous symmetry breaking and you get a concave and convex surface pair.
this unstable equilibrium at flat can be made stable by using 3 surfaces, A,B,C and going through AB, BC, CA, and repeat, so that the only valid solution becomes an optical flat (but this is not how your window panes are made, they simply float liquid glass on a molten lead bath)
If I understand you, you're saying that you get symmetry breaking instead, so that once it starts with either concave-convex or convex-concave, it continues going down that route.
Is that right? Is there a way to predict whether you get convex or concave on top, or do you just look at it after a while and say, "Huh, today I got one of these. Guess that's what I'll be looking at for the next N weeks of this project".
"The mirrors start as a flat disk of glass, typically plate glass or borosilicate glass (Pyrex).[4] The disk is carefully ground, polished and figured to an extremely accurate shape, usually a paraboloid... The tools used to achieve this shape can be simple... Through a whole series of random strokes the mirror naturally tends to become spherical in shape. At that point, a variation in polishing strokes is typically used to create and perfect the desired paraboloidal shape.