The latest XKCD What-If post discusses how one cannot start a fire by focusing the light from the moon.
The answer is no, for well-established reasons, but the explanation isn't watertight.
Maybe you can't overlay light rays, but can't you, you know, sort of smoosh them closer together, so you can fit more of them side-by-side? Then you could gather lots of smooshed beams and aim them at a target from slightly different angles.
Nope, you can't do this.
It turns out that any optical system follows a law called conservation of étendue. This law says that if you have light coming into a system from a bunch of different angles and over a large "input" area, then the input area times the input angle equals the output area times the output angle. If your light is concentrated to a smaller output area, then it must be "spread out" over a larger output angle.
In other words, you can't smoosh light beams together without also making them less parallel, which means you can't aim them at a faraway spot.
But the spot doesn't have to be faraway. From the diagram above, one could perhaps hold a piece of paper extremely close to the smaller area, so that even though the light is more directionally spread out, it doesn't matter because it hits its target after a negligible distance.
It seems to me that this effect isn't important -- one should be able to focus the sun/moon to a higher temperature based on this principle.
Why doesn't this argument work?