Why is silver such a good reflector of visible light?

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Metals are often good reflectors because they have a free sea of electrons that can slosh around in response to an electric field. Another way of saying this is that the energy levels of each atom become overlapped and form wide bands of possible energy levels for an electron. Therefore electrons can absorb and then re-emit photons over a large range of energy levels and not just at certain discrete energy levels like other materials without the sea of electrons (glass for example).

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Edit: I just saw you asked why is silver better than other metals? I think one of the main reasons it that it is somewhat resistant to corrosion and there are really nice ways to deposit silver on glass using chemical reactions: https://www.instructables.com/Make-Glass-Mirrors-With-Silver-Nitrate-Sugar-Am/

That'll work, but you'll have a lot of work milling it to optical standards I think.  Not that it needs to be telescope flat (within a wavelength, interferometrically), but it better be a good program and a tight mill.  Or use a lathe with a tightly adjusted curve cutter?

The other downside is tin will tarnish, and it's very soft so it will scratch extremely easily as well.  It might be reasonable to silver plate, in which case the tarnish may develop more slowly, and be easier to deal with (it should be a relatively heavy plating, to account for wear due to polishing, and for diffusion into the tin, which will slowly dissolve it from the underside).

As for alloys, 110 copper is cheap enough and easy to work, I guess.  A good lead-free tin candidate might be the stuff used for soldering plumbing (typically 95%, Sn 5% Sb).

If you're feeling more adventurous about casting, you could try making up some white brass, which will still tarnish, but will be much harder (scratch resistant).  Or the original: speculum metal (I think around 20% tin bronze, which is white, and very brittle -- you may need to grind rather than machine it).

Anything brass or bronze of course requires a furnace capable of 1200C, and all the handling equipment.  Any alloys containing zinc give off fumes when molten, use strong ventilation and avoid the fumes.  Guessing you don't have quite this much equipment... but if you do, it's certainly possible at home!

Tim

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