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This works because you're just concentrating the image of the sun. It's the surface temperature of the sun that matters. Now if, instead, the mirror were scattering or absorbing and re-radiating the light (as the moon does), then its temperature would be limiting factor.



Now if, instead, the mirror were scattering or absorbing and re-radiating the light (as the moon does)

Are you saying that mirrors do something other than absorbing and re-radiating light? In most explanations I've seen, this is exactly what they do:

How does the mirror reflect light? The silver atoms behind the glass absorb the photons of incoming light energy and become excited. But that makes them unstable, so they try to become stable again by getting rid of the extra energy—and they do that by giving off some more photons. (You can read about how atoms take in and give out photons in our article about light.) The back of a mirror is usually covered with some sort of darkly colored, protective material to stop the silver coating from getting scratched, and also to reduce the risk of any light seeping through from behind. Silver reflects light better than almost anything else and that's because it gives off almost as many photons of light as fall on it in the first place. The photons that come out of the mirror are pretty much the same as the ones that go into it.

https://www.explainthatstuff.com/howmirrorswork.html


I haven't done material physics in depth, so can't be 100% certain of this, but I don't see how that can be true. Electromagnetic reflection is what results in either specular reflection or diffuse reflection (i.e. scattering), not absorbing and re-radiating. Which is why the color of reflected light is dependent on the color of incoming light, and not on the spectral frequencies of the material (unlike re-radiated light).




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