Does the size of the atom limit the focal length of telescopes? Does the size of the atom place a theoretical limit on a telescope's focal length (and thus, resolution)?

It seems to me that that the allowed margin of error for parabolic mirrors drops with an increasing focal length. It's already like 25 nm for advanced Earth-based telescopes - which is just 50-250 atoms.

If we try building mirrors with an ever increasing focal length (e. g. as a part of a huge space-based interferometer), will we eventually reach a point where the precision required will be less than the size of the atom and thus no longer achievable? If yes, how far away are we from this limit now?

If we had unlimited resources, would it be possible to construct a space-based telescope for imagining extrasolar planets in great detail, or would this be not even theoretically possible due to the fixed atom size?
Ok, finally I can explain it. Not sure why it took so long.

Bottom line, for visible light atoms don't matter. Let's say the blue side of the visible spectrum of light has a wavelength of 400 nm (round number for simplicity). Let's assume the distance between two atoms in glass is 0.2 nm.

The thing is, light is a wave. Anything smaller than about 1/4 of a wavelength becomes essentially invisible to that wave. It's not a sharp threshold, but as things get smaller and smaller, the wave "sees" them less and less. It just goes around the object as if it's not even there.

1/4 wave of visible light is 100 nm, which is 500 glass atoms.

I make telescope mirrors. I can still see the effects of surface errors down to about 1/20 ... 1/25 of a wave. Beyond that the image is not really distinguishable from a geometrically perfect mirror, either in real-life tests under the stars, or in the lab using the equipment. Maybe an interferometer could push that limit a bit further, but not a whole lot.

Let's say the absolute measurable limit is 1/50 wave, which is 8 nm, which is 40 atoms. That's plenty of atoms. Any defects smaller than that simply do not change the image created by the mirror - when talking about regular telescope mirrors.

The surface level difference from a single layer of atoms does not even register in visible light. It takes far more thickness than that to make a visible difference.

So your ultra-long focal length mirror would be almost flat, slowly adding extra atomic layers towards the edge. As long as it approximates the desired ideal surface (paraboloid, etc), then it will be fine.

I see one exception. If the focal ratio is indeed so big that there isn't enough curvature in the surface to require even a single extra layer of atoms at the edge. Then, indeed, the mirror would not work, because it's flat down to the atomic level. Keep in mind though, that would be a mirror with a humongous focal ratio - and indeed with a cosmic-scale focal length. There are many issues with such a system before you even begin thinking about surface errors. Probably not feasible with current technology.

But then what you would do is make a segmented mirror, increasing the apparent diameter and reducing the focal ratio. You could even have multiple flat segments (flat down to the atomic level) but far from each other to massively increase the total diameter, and slightly tilted according to the shape of the ideal surface. If you can afford a cosmic-scale focal length, then you can surely afford a cosmic scale diameter, and that's how you reduce the focal ratio. Maintaining that precise tilt angle between segments would be a tremendous feat of engineering.