[dvh]

If a YouTube video I saw whether you can use moonlight to start a fire is to be believed, you cannot achieve higher temperature using lens than the source temperature, so your earth lens will achieve same temperature as 5cm lens from dollar store.

[hutzlibu]

But isn't the actual source the sun (6000K) and not the moon as it is acting only as a mirror?

With a mirror you can also burn things if you focus sunlight, but the surface of the mirror stays cool.

[ben_w]

At a guess, the moon is a diffuse rather than a reflective surface, so it's going to be closer to a maximum of the lunar surface temperature than to solar surface temperature.

An atmospheric lens, however, will reach a maximum of somewhat closer to solar surface temperature, though still lower because of scattering and absorption which definitely isn't trivial on this kind of scale.

[PaulHoule]

The moon is pretty dark, reflecting about 12% of the sunlight that falls on it

https://www.universetoday.com/19981/moon-albedo/

If it had an albedo of 0% it would be a black body and be radiating only thermal radiation at its surface temperature; it's not too far away from that but it is reflecting some "black body" radiation from the sun representative of a higher temperature.

[bartislartfast]

a 5cm lens from a dollar store can burn things in the focal point