Q: How do lenses that concentrate light not violate the second law of thermodynamics? If you use a magnifying glass to burn ants, aren’t you making a point hotter than the ambient temperature without losing energy?

Physicist: This is a surprisingly subtle question.

It certainly impossible to create new energy, but there’s nothing to stop you from piping energy from one place to another (say, by running hot water from a boiler to somewhere else).  The case of sunlight and a lens is just a matter of controlling where the energy is going in a slightly more abstract way.  Focusing light from the Sun doesn’t decrease entropy, because what a lens does (this is a little hand-wavy) is to exchange “direction information” for “position information”.  The light from one direction (from the direction of the Sun) gets brought together in one position (the focus).

Parallel light

Perfectly parallel light can be focused at a point, but light from different directions focus at different points.  Light from multiple directions can’t be focused to one point.

So, if the light from the Sun weren’t so parallel we wouldn’t be able to use a lens to focus it so well.  This is why, on a cloudy day, you can’t burn things with a magnifying lens, even when it’s fairly bright outside.  The energy is still there, it’s just scattered.

A little surprisingly, focusing parallel light to a point does not change the entropy of the light, and there’s a cute way to show that.  A good rule of thumb for entropy is, “if you can reverse it, then the entropy is constant”.  In this case, were you so inclined, you could put a second lens after the first that “re-parallelizes” the light.

The act of focusing light is reversible, so it doesn't increase entropy.

The act of focusing parallel light is reversible (here’s how), so it doesn’t increase entropy.

It seems as though there should be some way to bring together lots of light beams using lenses and mirrors and… optical cables or something, that would allow you to get a tiny region as hot as you want.  But as it happens: no.  This is yet another example of the universe having an obnoxious no-go law.

There is a general thermodynamic rule which says that you can never focus energy in such a way that the target is hotter than the source.  So, no matter how many mirrors and lenses you have, you can never focus sunlight in such a way that it’ll be hotter than 5800K (the surface temperature of the Sun), but you can get close.  In practice that isn’t too useful, because machines tend to break at surface-of-the-sun temperatures.

If you were in the bright

If you were in the bright spot you’d see a bigger image of the Sun through the lens.  With more directions that end in a hot source, the focal point gets hotter.

A good way to think about this is to imagine yourself meandering about in the surface of the Sun, and then imagine yourself lounging at the focus.  If you were in the upper layers of the Sun, you’d notice that in every direction you look there’s material radiating at around 5800 Kelvin.  As a result, you’d find yourself equilibrating to that same temperature (and burned up real good).  If you were at the focus of an elaborate set up of mirrors and whatnot, then you’d be in the same situation, with every direction you look ending with the Sun.  And the result is the same.

It feels like there should be some way to cheat, but there just isn’t.  If you could find a way to get your target hotter than the source, then you’d have yourself a genuine over-unity device!

The magnifying glass picture is from here.

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25 Responses to Q: How do lenses that concentrate light not violate the second law of thermodynamics? If you use a magnifying glass to burn ants, aren’t you making a point hotter than the ambient temperature without losing energy?

  1. Raimundo Martins says:

    Are you sure you get an over-unity device? Because if you focus you’re energy, matter around the focus will not receive that energy.
    You just have higher energy-density, not more total energy. Is there any proof/experiment of that statement? I just don’t this as impossible, nor useful.

  2. The Physicist The Physicist says:

    You’d be able to pump heat from a low temperature to a high temperature system at no cost whatsoever. Then you just plug in a regular heat engine (of whatever form) to catch the flow of enery back to the lower temperature system, and you’ve got free usable energy!

  3. Raimundo Martins says:

    Still, that doesn’t make it over-unity. You just transformed energy! The low temp system got cooler, and so did the high temp. It doesn’t mean it’s more than what you had at the beginning.
    The point being it would be possible to extract energy from a low temp source, making it cooler and cooler. Now that I think about it, this might decrease entropy or something like that. Bah, I never liked thermodynamics much, anyways :P
    But still, I wonder from which equations this can be proven, since conservation of energy isn’t necessarily the problem.

  4. Greg says:

    Here’s a load of mirrors that reflect sunlight to get up to 3,500 degrees C which is pretty cool!
    http://en.wikipedia.org/wiki/Solar_furnace

  5. Ryan Callahan says:

    What if we surround the sun with a Dyson Sphere covered in mirrors that reflect all of the light from the surface of the sun to one point on a small asteroid?

  6. The Physicist The Physicist says:

    It’s harder to keep track of why a more complicated model like that wouldn’t work, but the idea is the same. Each of those mirrors would have to deal with light from a wide range of angles, and that means that they wouldn’t be able to focus very well.

  7. Mike Winston says:

    Is there some sort of way to quantify your ideas of information about position and direction?

  8. Ryan Callahan says:

    Imagine a point M, whose position is being measured several times, within a set of different possible boundaries:

    W—M—X——-Y——-Z

    The information content of the measurement I(W,Y) is related to the information content of the measurement I(W,Z) as

    DeltaI = k*ln((Z – W)/(Y -W))

    And to I(W,X) as

    DeltaI = k*ln((X – W)/(Y – W)

    Which is negative.

    I imagine the same is true of momentum, where momentum is considered in terms of its magnitude on a number line.

  9. Ryan Callahan says:

    Also, what if the Dysonsphere is

    a. Contracting

    b. cleverly shaped and rotating, with its mirrors potentially also rotating, in such a way as to bring two seconds of the sun’s energy to the asteroid in one second.

    c. Using some of that energy to pump heat from the rest of the sun onto the asteroid

    Or

    d. The asteroid is contracting.

  10. The Physicist The Physicist says:

    That’ll do it. But keep in mid that you have to do work to contract the sphere. Similarly you can raise or lower the temperature of any system if you have access to pumps that do work.

  11. Ryan Callahan says:

    Oh, hey Physicist, magnitude of momentum on a number line wouldn’t cover all of the information in I(momentum measurement) would it?

    I(max inertia, min inertia) + I(theta, psi) = I(p-observed)

    …where theta and psi are spherical coordinates, seems plausible.

  12. Jason Borchard says:

    I’m going to have to disagree that using energy from the sun one could not raise an arbitrarily small amount of matter to a temperature above 5,800K. Temperature as it is usually conceived is a bulk property of some material, but it actually refers to the differential in kinetic energy between locally interactive massive particles (in practical terms no smaller than atomic scales). Using solar panels on only a small fraction of the surface of earth, one could achieve enough voltage and current to power a laser that could heat some material sample to the plasma phase transition and higher.

    The second law of thermodynamics is statistical in nature. The extraordinarily low entropy of your brain, for example, which has allowed humans to calculate and record decimal approximations of pi to billions of digits, for example, seems to violate the second law. In actual fact, plants photosynthesized reduced carbon compounds (sugars), and our ancestors ate them for hundreds of millions of years, building up a vast (low entropy) store of information (46 chromosomes), that now codes for a brain and dexterous hands which build cities of skyscrapers, which build refrigerators and compressive heat pumps. In terms of steam engines and phase transitions thermodynamics isn’t two complicated. In terms of genetics, computability theory, and quantum information theory, it is quite mysterious.

  13. Larry Dale says:

    Jason, I am a layman, but I think where your mistake is that the oriiginal item was about mirrors focusing the rays of the Sun only. Once you start inserting other bits of equipment then you are no longer dealing with Sunlight directly. You are converting one form of energy into another and by the time the laser is activated the source is now way back down the line. If this were not so then one could recycle the source to achieve a Perpetual machine.
    With regard to human beings then as a practicle unit we have a higher level of disorder than say some microbe. Depends what criteria we are using. There are so many ways that a human can suffer because of the large number of ‘sub-units’ that can be disrupted. This is perhaps the price we pay for intelligence. Considering the large amounts of energy we require every day I would view that as an example of a high entropy organism.

  14. Pingback: Pourquoi une loupe ne viole pas la thermodynamique | Pourquoi Comment Combien

  15. FZL. says:

    You focus the light , i.e you change the density of energy. now there is just the difference in densities of energies on both sides of the lense. AND no net gain so no violation . in other words there is just difference in the AREAS the light is striking.

  16. Edward Zeile says:

    In a very old issue of Scientific American I read about something called an anisotropic mirror that focused the light from the sun to where the temperature reached was over
    Fifty thousand degrees. It did not form an image of the sun at the focal point. It
    Converged portions of that would be image on top of one another. Lets say that the
    Sun was a pumpkin pie cut into 12 slices, the image that would appear would not be
    the sun cut into 12 slices. The image that would appear would be 12 slices all concentrated into one slice. The image did not look like the original pie. It looked like a very bright blob of light.

  17. AlexD says:

    Could a series of Fresnel lenses not be used to “re-parallel” the light from multiple sources before attempting to focus the light?

    my thoughts are sun to plano-convex (to capture as much light from the various angles of the sun without complex angling mechanisms)/fresnel lens (to re-point the light in a uniform direction) combo, on to a secondary plano-convex/fresnel lens (to allow for several of the first instances to be aimed at the secondary instance) on to one convex lens to focus the light onto a single point.

    In my head it’s like spotlights on a stage, with the performer being the seconday plano-convex/frenel combo lens?

  18. Dan says:

    Your example with not being able to heat something hotter than the suns surface temperature using magnifying glasses and mirrors seems flawed to me. It seems like you’re saying the best you could do is replicate the incoming energy at any point on the surface but standing on the surface, you’re only receiving energy from the whatever portion of the sun is not beyond the horizon of the sun. From your point of view. With mirros, though, you could bounce around light and energy from the other side of the sun as well.

  19. Ryan Callahan says:

    Yeah; what if you took the light from one side of the sun, and reflected and magnified it onto a point on the other side of the sun?

  20. Xerenarcy says:

    explanation in 30 seconds:

    1. heat transfer is just that, a transfer – to heat something further than your heat source, you need a hotter heat source, or extra thermal energy from somewhere else (eg, exothermic reactions). if this was not the case, you could (for example) boil water with your body by concentrating the blackbody heat from it into a sufficiently small region.

    2. a lens only changes the direction of light, the energy passing through it is unaltered. if not, the lens would undergo some sort of change as well, heating up or cooling off (absorbing or releasing energy respectively)

    3. light has no problem congregating in one location unlike most particles, photons very rarely interact with eachother directly (ie, at energies high enough to create particle pairs or neutral particles; visible light has relatively tiny energy per photon). this means that photons crossing eachother’s paths will, for the most part, not interact, and just keep going. this is apparent by the image being inverted after passing through the focal point of a lens, but is otherwise unaltered.

  21. Ryan Callahan says:

    You’re not saying the light would pass through the sun if you reflected it back onto the sun are you? I’m pretty sure that’s not what would happen. If you put rocks around a fire pit, it seems to help keep a fire going even if there’s no wind for the rocks to protect it from… the heat in the rocks is being reflected back into the fire, which makes it hotter than if there was nothing there to radiate the energy back into it.
    I just don’t see what is fundamentally different from taking the light from two places on the sun and reflecting them onto the same point, and taking the light from one part of the sun and reflecting it onto a different part of the sun. The light already got “reflected” (to use the term a bit loosely) onto the surface of the sun from the core, by the particles it ran into on the way.

  22. The Physicist The Physicist says:

    @Ryan
    What you’re describing is a situation where the Sun is insulated from space, by keeping the light in. Mylar blankets do exactly the same thing. The temperature at the surface is a balance between the cold of space and the ludicrous heat of the core. Taken to an extreme, with a silvered Dyson sphere, a star with all of its light reflected back onto its surface would heat up (because stars make new heat) but would eventually equilibrate with the entire Sun fixed at very nearly the same temperature.
    Same thing with stones in a fire: basically just a layer of insulation. Insulated heat sources do get hotter, but not for any fancy thermodynamicy reasons.

  23. Ryan Callahan says:

    Hm. What if you covered the dysonsphere with fiberoptic cables which piped all the light through a series of two-way-mirror-check-valves (to prevent energy from flowing back out) into a small (very strong, very well insulated) container? I’m sure Mama Nature has a clever solution for that one too, but I can’t think what it would be.

  24. The Physicist The Physicist says:

    The fiber optic cables would need to be wider at one end and thinner at the other. The effect would be a bunch of light spilling backward. At the end of the day, there just aren’t any one-way energy valves (no Maxwell’s demons).

  25. Ryan Callahan says:

    The universe is so mean!

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