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theoretically could you build a large enough lens to concentrate moonlight to start a peice of paper on fire. My 16 year old son and I are locked in this debate and we need an expert opinion.
- Glen Hawkins (age 44)
That's a very intriguing original question. I think the answer is no.
There are several ways to make the argument. They all rely on a key fact- that the moon scatters the sunlight that hits it into more or less random directions. That greatly limits the ability of any subsequent optical device (lens, mirror,...) to refocus the light.
Here's one argument. Let's imagine that the moon's surface was hot enough to glow with the same energy intensity as we actually see in its reflected sunlight. (The spectrum would be different, but that's not very relevant for the heating power. The important point is that the thermal radiation also heads off in all directions.) No passive device (such as a lens) could cause this thermal system to spontaneously heat up another system to a temperature higher than the surface temperature. How hot would that surface temperature be? Since the moon is at about the same distance from the sun as us, and we are at the right temperature to emit about as much radiation as hits us from the sun, that means that the focused moonlight would only heat things up a little above ordinary room temperature. (I've used the law that the absolute temperature only goes as the 1/4 power of the thermal radiation flux to get that even adding the focused moonlight to our ordinary radiant energy wouldn't get things very hot.)
That was fun- took some thought.
(published on 10/21/2011)
Follow-Up #1: flashlight burner
I have a 2 000 000 candelas portable halogen flashlight. I'm able to burn things with it when I focus the light on a dark surface with my magnifying glass. Surely with a large enough magnifying glass I could also do the same with moon light.
No, this actually makes sense.The filament of your halogen bulb is very hot. With good clear optics, you should be able to get something else nearly as hot as the filament. The surface of the sun is also very hot, so that's why with good optics you can use sunlight to also burn paper. The surface of the moon is cool, and radiates only as much as a lukewarm object. You can't use its light to burn paper.
If you were to put some frosted glass a few inches in front of your halogen bulb, diffusing its light like the sunlight bouncing off the moon, you'd find you couldn't burn paper with it either.
(published on 10/23/11)
Follow-Up #2: unfocussed light
Say the energy intensity of reflected light is x watts per sq.in off the moon's surface S. If you have a magnifier glass with surface also S (as big as moon) located close to the moon then you have x watts going through each sq.in of the glass. This means the glass is emitting x watts per each of its sq.in. Now if you focus this energy to an area s of paper, then according to conservation law of energy, you will have to have S/s * x watts of energy falling on each sq.in of paper. For example, if S/s is 1,000,000 then each sq.in of paper will receive 1M Watts. So the question simplifies to will 1M watts per sq.in burn the paper? If not then s can be reduced (focus sharpened) to reach S/s * x watts that is enough to burn the paper. I say, the answer is yes.
- Mehran (age 61)
Hi Mehran- It won't work because the light is heading all different directions so it won't focus. The product of the angular range and the spatial range stays constant as you manipulate the beam with lenses or mirrors. So you can take a spread-out beam traveling in nearly complete collimation and focus it down to a small spot, with the beam at the spot coming in from a wide range of directions. Here you start out with a wide range of directions and
positions, so you're out of luck.
(published on 02/25/12)
Follow-Up #3: focusing moonlight
The light from the sun is also heading in all different directions.. It will focus down to an image of the sun, and likewise the moonlight will focus down to an image of the moon. I think that the answer to this question is in fact yes.
- Kevin (age 50)
Newark, DE, USA
Both the sunlight and moonlight head out in all directions. With optimum focusing of either one, you can get a radiant energy flux at the focus that's about the same as the radiant energy flux at the surface where it came from. In the case of the sun, that energy flux is what's radiated by a roughly 6000K surface. In the case of the moon the net energy flux is very roughly equivalent to what would be radiated by a 300K surface. That's a big difference. So you can easily start fires with focused sunlight but not moonlight. Try it!
(published on 03/01/13)
Follow-Up #4: burning paper with moonlight?
Since it is generally accepted that bright moonlight flux is approx 1/5000000 that of the accepted solar standard used to calculate photovoltaic device efficiencies (1-sun at 1.5 air-mass = 1000 watts/sq. meter), moonlight insolation striking the earth's surface equates to (1000W/sq.meter x 1/500000) = 0.002W/sq.meter. So, if you used a 5.0 sq/meter lens to focus that moonlight down to a 1.0 sq.cm spot, the resultant flux intensity would be 100 watts/sq.cm, which is probably enough impinging concentrated radiant energy to ignite a black piece of paper. -KPS
- Kevin S. (age 50)
Newark, DE, USA
The general outline of your calculation makes sense, and the relative size of the image and the lens is also consistent with optical laws. The problem is right at the end, where you accidentally switched meters and cm.
0.002W/sq.meter * 5 sq.meter= 0.01 W.
So in your 1 cm2
image, you've only got 0.01 W/cm2
or 100 W/m2
. That's only around 10% of what you get from unfocussed
sunlight. It won't burn the paper.
(published on 03/05/13)
Follow-up on this answer.