This week’s xkcd What If asked if a magnifying glass can be used to start a fire with only moonlight. Randall’s answer is no, the primary reason being that lenses and mirrors can’t make something hotter than the surface of the light source itself. It’s worth reading the explanation of why that’s the case; I had mistakenly thought it was possible to “concentrate” the heat into a smaller area, so ignorance fought there.
But I’m not following why that pertains to the Moon, which is reflecting light from a different source. Randall even calls this out:
But he doesn’t “get to it later” to my satisfaction. I’m still not seeing why the temperature of the Moon’s surface is a boundary on the possible temperature achievable with a lens. If the Moon were a perfect mirror, I’d expect no heating of its surface from the sun, and I’d be able to capture the perfectly reflected rays with a lens and heat something hotter than the Moon’s surface. Even as an imperfect reflector, the Moon is acting as part of the optical system, not a light source.
I’m not disagreeing with the final answer that moonlight can’t be used to start a fire, but is his explanation relating it to the surface temperature of the Moon correct? I think the reason is that too much light is lost due to absorption and diffuse reflection.