Physics · the experiment
Grind your mirror into a sphere
Two glass disks, some grit, random strokes. Set the length of the stroke and watch a mirror's surface turn smooth, then spherical.
1 · Smooth first
Beginner
You grind with the normal stroke. Which defects of the surface fade first?
2 · Time to a sphere
Intermediate
With the normal stroke, the full travel is a third of the diameter, so R_stroke, half that travel, is R_mirror/3. With T_sphere = (32/π²)(R_mirror/R_stroke)² T_grind, how long does spherizing take?
Find it in the simulation: set the stroke so that the measured T_sphere equals what you just worked out.
3 · The tumbled pebble
Expert
In a rock tumbler, the pebble plays the role of the mirror, and (R_rock/R_stroke)² is about 100. How many times longer than a mirror with the normal stroke does it take to become a sphere?
Switch to the tumbler: set the stroke to the pebble's, and watch what fades, and when.
4 · Why not longer?
Expert
A longer stroke spherizes faster. So why do mirror makers still finish the sphere with the normal stroke?
Spherical mirror
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