Can we use moonlight to start a fire?
How large of a magnifying lens would you need in order to focus enough moonlight to start a fire?
There is actually a limit to how much you can magnify the light in an object with a lens because of a fundamental law of optics that says:
"In order to make something appear, let's say, ten times brighter, you have to make it appear ten times bigger in the sky."
So when you use a magnifying glass to make the sun appear perhaps 30 times brighter to set fire to a piece of paper, what you're actually doing is making the sun appear to take up 30 times the area of the sky from the piece of paper's point of view. Now, obviously you reach a hard limit when the sun's rays are coming from all directions in the sky towards your piece of paper. It's perhaps interesting to ask what temperature your paper would reach if you have a lens that could do that. And the answer is the paper would see a view of the universe, just as if it was embedded in the surface of the sun. And so, it reached for the same temperature that the surface of the sun is at, at about 6,000 degrees C.
Now moving that to the moon, the surface of the moon has an average temperature of about minus 50Ã?,°C, so that's actually quite cold. So even if you covered the whole sky with moonlight and had no sun, your piece of paper will reach a temperature of -50 and no warmer. So no, you couldn't use the moon to set fire to a piece of paper.
There is an interesting extension to that because if we think of stars as being much fainter than the moon, but stars are also much smaller. So if you magnify the light of the star up to fill the whole sky, you'll reach the temperature of the surface of that star. You could potentially use a star to set fire to a piece of paper. And in fact, there is a paper that was published in 2002 with a design of a telescope for doing exactly that.