After a chat with light transport fellows, I realized that it is not a well-known fact even among professionals that the entropy in the optical system cannot decrease (2nd law). That’s why you cannot start a fire from a moonlight using just optics https://what-if.xkcd.com/145/
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Optics makes people stupid. Given a far-away light source that transmits light energy E to a given area, you can always position n mirrors around the object to project n*E energy onto the area. If the light’s blackbody temperature exceeds its combustion temperature, it’ll burn.
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This is only true for a point source. But the moon isn't a point source - it has an area that is very significant in this case. So the energy never gets concentrated more than "the surface of the moon". Which isn't very hot.
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Again, color temperature is not temperature, and being surrounded by lunar light does not heat you to 4000K.
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(Color temperature is not temperature.)

