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This question already has an answer here:

Randall Munroe posted an interesting what-if in which he claims that you can't use moonlight to light a fire, because it is impossible for reflected light to raise the temperature of an object higher than that of the reflecting surface, which of course is obviously false.

I continued thinking about the problem, and read a couple of other questions on the topic, and I'm not asking (as those questions do) whether it is possible, as it clearly is, but how you could do it.

So, here is the scenario: You are in an open plane with no obstructions (trees, clouds, buildings etc) between you and the sky. The moon is full. You can magically suspend a lens of any size and shape anywhere between you and the moon (but any sunlight that hits it mysteriously vanishes - moonlight only!). You are attempting to set fire to a piece of paper.

How big would the lens need to be to achieve this?

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marked as duplicate by valerio, Red Act, Jon Custer, Cosmas Zachos, Emilio Pisanty Feb 28 '18 at 17:31

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ You accept that it is not possible, but then ask how to do it? You are basically asking for how to break the laws of thermodynamics. $\endgroup$ – Anders Sandberg Feb 28 '18 at 16:39
  • $\begingroup$ @AndersSandberg No, if you read carefully OP is assuming that it is possible. Anyway, this is still a duplicate in my opinion. $\endgroup$ – valerio Feb 28 '18 at 16:41
  • $\begingroup$ Why is it "obviously false"? Randall Munroe only claims that it's impossible for a passive optical system, due to conservation of etendue. The duplicate question agrees here; if you have an active system that can store and release energy (i.e. solar panels), then you can definitely set fire to something, but at that point you're not using moonlight to set something on fire, you're using moonlight to charge a battery. $\endgroup$ – probably_someone Feb 28 '18 at 16:58
  • $\begingroup$ @probably_someone it's "obviously false" because the argument hinges on it being impossible for reflected light to raise a temperature higher than the reflecting surface, which is easy to disprove - just use a mirror to reflect sunlight into a lens, and you'll find you can easily heat a point to a higher temperature than the mirror. Or point a laser at a mirror and observe as it is reflected. $\endgroup$ – Benubird Mar 1 '18 at 10:13
  • $\begingroup$ I think you need to read the what-if more carefully. It's impossible for reflected light to raise the temperature higher than the temperature of the light source. (The moon is a diffuse reflector, so you can't count the sun as the light source here, even though moonlight originally comes from the sun.) $\endgroup$ – ptomato Mar 1 '18 at 23:59