Will it work? Could you do the same to an oven?
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I don't know how hot campfires get, but let's take 1000K as a nice round number. The Planck distribution for 1000K looks like:
(Calculated, as the logo suggests, using this web site.)
In my answer to Can a glass window protect from heat radiation? I post this graph showing the transmission of glass in the IR region:
And this shows the transmission falls rapidly for wavelengths above 2 $\mu$m. Looking again at the distribution for 1000K most of the energy is at wavelengths above 2 $\mu$m, so while the lens will be able to focus some of the radiation from the campfire most of the energy will be lost to absorption in the lens.
Focussing the radiation from the Sun is effective because the radiation from the Sun peaks in the visible wavelengths and the majority of the radiation makes it through the lens. In principle focussing radiation from a campfire would work as well, but you'd need the lens to be made of some material that did not absorb IR radiation.
John Rennie
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The sun is so far away, almost all the light hitting the surface of a magnifying glass is traveling in the almost exactly same direction, that helps make the light focus-able to a point. When you try the same thing with a close-by object, you get an upside down picture of the object, so it's far harder to focus the light from a near by source into a point and you really need it focused to a point to use concentrated light as a method for igniting something on fire.
You'd need an enormous number or size of focusers/reflectors to have any hope at all and, even then, I'm inclined to say it would be virtually impossible. Fire is obviously less bright than the sun. People like looking at fires, we sit around the camp fire and it doesn't hurt our eyes. It's barely bright enough to read by. I've never known anyone who likes to look at the sun.
Here's a similar question about the moon - which has the advantage of being far enough away that moon light could be focused, for all practical purposes into a point, but as you can see by the answers, you don't get enough light from the moon. You'd need a very large magnifying glass.
