Why check the maths, the concept is right there at the start,
if you concentrate the light, its the same as concentrating heat… and that makes for a high temperature.
The temperature difference is not allowing “energy from nowhere”, the power is from the thing radiating all that power to start with. Just its gone via the lenses to the other thing
The argument has been thoroughly discussed from a thermodynamics standpoint, but from an optical standpoint, you can’t make a 36-ft diameter lens that concentrates all the light it receives onto a 1-inch circle (i.e. a 10 ft focal length). If you try to build a Fresnel lens like this, you’ll find that the lens facets towards the edge will block each other. To avoid this, you’d need facets that take incoming light and squeeze it into a tighter bundle than the incoming light, which is optically and thermodynamically impossible.
Seen from the focus, looking back at the lens, the lens appears as a big circle with the same surface brightness as the sun, only larger. With an arbitrarily large lens, the lens looks like an entire “sky” (hemisphere) at the same surface brightness as the sun. If you achieve this, the focus can reach the same temperature as the sun. There is no way to go beyond that.
Imagine a white hot furnace. The walls of the furnace are literally glowing white hot. You take a parabolic mirror, or lens, or whatever you like. Put the mirror inside the furnace. Put a thermometer at the focus of the parabola. Is the focus of the parabolic mirror inside the furnace hotter than the rest of the furnace?
The answer is no.
The mirror can’t add more heat to the focus of the parabola, because if the focus becomes hotter than the furnace it radiates heat back to the furnace. The furnace and the object at the focus reach equilibrium, and neither are hotter than the other.
Why is it optically impossible to squeeze the light into a tighter bundle than the incoming light? Isn’t that what a reflector telescope does - bounce light off of two mirrors and concentrate it into a tighter beam before it passes through the eyepiece?
I find this a fascinating question because I seem to be able to find arguments that support both sides, and I’m trying to find out which assumptions are wrong in the wrong argument. I can see that heating a test object hotter than the heat source should be thermodynamically impossible, but I can’t get past the idea that at the same temperature the heat source is radiating more total energy than it receives from the test object; if each are blackbodies, why doesn’t the test object heat up?
CalMeacham mentioned the answer in post #8: etendue.
In simple terms, etendue is the degree to which light crisscrosses itself in flight. A laser beam has zero etendue, because the light is moving in exactly parallel beams. A zero-size spherical radiator also has zero etendue because the beams all move radially outward. The sun however has non-zero etendue, because it is a ball with spatial extent. The light from one side of the sun crosses the light from the other side.
The math is tricky, but you can demonstrate that you can never get rid of the crisscrossing. Put another way, no optical system can reduce etendue–it can only increase.
Light flowing into a zero-size point has zero etendue. But our source–the sun–does not. Therefore it’s impossible to build an optical system that accomplishes this. There’s some greatest minification of the light and it turns out to be the point where the spot gets as hot as the sun’s surface. Which is really just a long-winded way of saying that the Second Law of Thermodynamics is true.
I don’t think this is actually true: It might be very low, but it won’t be zero.
I can see this to be true in a linear optic system. However, generally, one can use the sun energy falling on a given area to concentrate a beam to to a point of very high temperature indeed. This without storing any energy. The OP did not state anything related to standard lenses or reflectors.
For instance one can convert part of the solar energy with solar panels and operate a high power laser. One could even power such a laser directly from concentrated sunlight.
While I know very little about non-linear optics I don’t believe that the etendue limit holds there.
“Zero” is the simplified way of saying “the etendue of a laser beam can reach arbitrarily close to zero as the beam diameter approaches infinity” :). So yeah, it’s never quite zero for real-world beams, but it is very low. Likewise, you can never quite have a point source of light, but the entendue goes down as you approach that ideal.
Etendue is the way that the 2LoT is enforced in a purely optical system. With non-optical elements, like lasers and solar cells, the 2LoT is enforced in a different way. For instance, solar cells are subject to the Carnot limit for efficiency. Therefore, although you can use the collected power to generate a very hot beam, the efficiency loss in doing so guarantees that you can’t build a perpetual heat engine out of it.
I don’t know much about non-linear optics either, but at least some non-linear media (like the KTP crystals used to frequency-double IR lasers to green) should preserve etendue. If any materials don’t, they must have some other mechanism for preserving the 2LoT.
Well, OP’s question is not very well defined, but if, as I get it we’re in an open system (i. e. sun and space) we have enough temperature difference to spare for a few years. Even Sun vs Earth. So I’m not sure 2Lot is relevant here. For a closed system, yes, obviously.
The 2LoT is relevant because if you could build such an optical device, then you could use it to extract energy from a heat reservoir without a differential. It doesn’t matter if you don’t actually happen to be using it for that purpose–the laws of physics still prohibit it.
I guess I should have been more precise. It’s impossible for a passive optical system to take light from an extended light source, and bundle it into a parallel beam with higher power density. Which is equivalent to saying: a passive optical system cannot increase the apparent surface brightness of a beam.
A telescope does indeed take a bundle of light and concentrate it into a tighter beam. But to do this, the telescope must have a >1 magnification. So if you look at the sun through this telescope, the sun doesn’t look brighter, it just looks bigger, with the same surface brightness.
Not really. If you look at the arguments that appear to say it’s possible to heat something above the temperature of the sun, it’s all based on over-simplification or incorrect application of optics.
Only a tiny fraction of heat from the heat source is reaching the test object, while a large fraction of the heat from the test object is radiated back to the heat source. The actual amount is the same (which is why they are in equilibrium), but it represents a different percentage of the total radiation from each object.
Yes, it’s definitely possible to use solar panels to power a laser that heats up a tiny spot to a million degrees. I think in this case, we’re using energy to lower entropy, and laws of thermodynamics will limit how efficient such a system can be.
Thanks for your replies; it was the etendue that was messing me up. In retrospect I see that the optics I was thinking of would require the Sun to be a point source of light rather than a physical object with nonzero size.
I revived this a month ago to point out a new xkcd on point.
I’m reviving it again to point out a newer xkcd on point: Fire From Moonlight
Which in effect offers a correction, or at least a clarification, of what his first article meant (and didn’t mean).
His ew article nicely follows the lay confusion & professional clarifications that were posted here over the last month-ish.
Further making me wonder whether Randall (or his henchmen) monitor our site for interesting issues
I almost understood that…
Thank you for CONFIRMING EVERYTHING I SAID LAST YEAR.
I’m taking a victory lap here.
Lasers (and all electromagnetic spectra) have a fundamental divergence angle based on the wavelength and aperture. While you could in theory make a laser with arbitrarily low divergence by making a really large aperture (or collimating the beam with a large diameter lens), this also requires a lasing cavity of arbitrary width and the fundamental problems that go along with that. As a practical matter, laser beam that are diffraction limited (as collimated as practical) are treated as having a Gaussian irradiance distribution.
Lasers used to image the moon for the Lunar Laser Ranging Experiment at ~250,000 km distance use a wavelength of ~694 nm with an initial aperture of around 3.5 m. They diverge at about 1 arcsecond of angle and are ~2 km in diameter at the lunar surface. At interplanetary distances the divergence is even larger.
As for the original question of being able to heat an object using sunlight at a temperature greater than the radiating surface of the Sun, the answer is given by the same basic laws of thermodynamics that governed all statistical physics, chemistry, et cetera, and there is no way to work around or break these laws by some kind of clever engineering or creative bookkeeping. scr4 is correct that optically manipulating incoming light simply gives more detail by enlarging it, but does not increase the temperature or total irradiance. Any device that could do this would violate the laws of thermodynamics and would thus be magical, and despite the popularity of Harry Potter we don’t use magical devices or play polo on flying broomsticks in the real world.
Stranger
Divergence is not a problem in and of itself. An ideal pinhole emitter has high divergence, but zero etendue. However, an ideal pinhole has zero size and thus emits no light.
The problem is that for a real beam, these diverging emitters are spread out across a non-zero area, and thus their emissions cross each other (making a non-zero etendue). As mentioned, you can reduce this by making the beam diameter larger, but for any given diameter there is a lower limit.