Challenge Questions

The magnifying glass simply focuses light to a point, assuming that it is properly ground. The energy that can be concentrated at that point will be a function of the area of the lens and the unit energy per square centimeter from the source illumination. The effective radiation power is the square of the ratio of the angles created by the focal length. If the point is your eye (do not try this!!!), the apparent angular size of the Sun is no longer .5 degrees, but 10, 100, or 500 times larger. So the energy absorbed is greater by the square of that apparent angle versus the actual angle. I am not sure I am articulating that correctly.

The theoretical upper limit for the point temperature at the focal length is the same of the source of illumination, about 6000 degrees C for our Sun. No glass lens is 100% efficient and the resulting temperature will be somewhat less, regardless of the lens size. Even a lens the size of the Sun and no atmosphere will not do it. A bigger problem is that the energy deposited is also radiated back off the object, some of that is reflected light (you can't get 100% absorbtion).

Any object that is heated will dissipate heat and reflected energy. Even if you use a bank of mirrors and lenses to totally surround the object you want to heat the resulting energy at the point source can not exceed the surface temperature of the Sun. If it did the object would be brighter than the Sun and would therefore radiate more energy out than it received in. That can't happen because the object at the focal point reaches a state of equilibrium where energy in is the same as energy out.

That bet was not such a hot idea after all!

I agree with our Hero 100%, but my logic runs a little simpler. The frequency of infrared light is indicative of the temperature of the emiting object. So while you may be able to increase the BTU/unit-time input, the temperature is invariant. The only reason you don't burn a hole thru yourself is that the BTU input is so comparatively miniscule.

Your logic is definitely simple. But taking your logic a step further, the temperature on your hand should be "invariant" even if you don't use any magnifying glass at all. The temperature will depend primarily on intensity, which is BTUH/unit-area. Size matters!

One answer lies in the wording of the challenge, which refers to a spot ON THE OBJECT. A very large lens properly focused would quickly vaporize the target area of any substance I'm aware of, and the kinetic energy of the vaporized atoms or molecules would quickly remove them from the target area, until equilibrium is reached with the surface of the resulting hole in the target just below the vaporization temperature of the target material

The friend is right. It can't get hotter than the sun. Actually, the question contains an error. The focal length of the larger magnifying glass is longer, not shorter. (The foccal length of a simple lens can generally be no shorter than about half its diameter; f=1:2.) And it does not focus to a point. It creates an image of the sun, and the size of the image varies directly with the focal length. So the spot from the larger lens is larger, rather than "hotter", although the temperature of your hand will be higher because the heat loss from the large spot will be proportionally less than from from the small spot.

Correction: the focal length of a typical magnifying glass is roughly double its diameter, not half. Sorry.

some commentators have noticed the ambiguity here about energy versus temperature. and that about energy versus visible light. however, it is obvious that if we limit ourselves to an extremely narrow band of the electromagnetic spectrum, and have a lens the size of the sun, and focus that electromagnetic band on a single point, we are going to direct the sum of the energy or somewhere close to it on that single point and whatever is at that point is going to get much more energized than any point on the sun. whether it will get "hotter" is perhaps a different matter, depending on the specific heat of the material in question. certainly it is possible that it could get hotter than the surface of the sun in that narrow wavelength band, presuming it is able to absorb that energy. this again brings up another ambiguity, which is, what do you mean by the temperature at the surface of the sun? it does not have, specifically, a surface. nevertheless, one would obviously be able to concentrate more energy by focusing it. hotter does not mean more energy it merely indicates the relative direction in which heat energy is going to flow.

"Who's right indeed!" you exclaim as you whip out your billfold to tempt the other Dad with a fresh crisp $20 bill.

As soon as the wager is struck, you instruct your son to remove his iPod ear buds for a moment, so that he might learn how to extract an easy and legal $20 from a perfect stranger.

"Hotter than the surface of the sun is really not that difficult at all." You start with your new friend staring somewhat incredulously. "You see, the sun's surface, also called the photosphere, has a temperature range of from a mere 5,500 degrees C to 6,000 degrees C. and a luminosity in watts of 3.83 x 10 to the 26th power. The key to extracting that power is having a big enough lens to concentrate the light to a small enough area onto a material with a low coefficient of reflectivity and insulated enough to become a heat accumulator."

As you reach for the exposed edge of his $20 bill, he pulls his hand back. "Not so fast!" he countered effusively. "It just so happens that in 1931 a Chemist named Robert Browning Sosman did his level headed best to build a sun powered furnace for U.S. Steel and was only able to achieve about 3,000 degrees C. I doubt that you could do any better."

As you raise your hand to present the man his $20, you notice your son putting his ear buds back in as he mutters, "Good one, Dad!"

The new $20 friend slaps you on the back as you sheepishly examine the spot of light made by the magnifying glass on the back of your hand. "Ouch!"

Heat cannot flow from a lower temperature source to a higher temperature receiver. So, the highest theoretically feasible temperature at the focal point is that of whatever part of the sun that is being focussed. A.V.Ramani

you have hit the nail right on the head. end of story.

...But we're talking Energy flow - how about a CO2 laser running at about room temperature, but melting through steel?

I agree! Temperature can't flow upscale. Good one.

Temperature doesn't flow anywhere - it's just a measurement of one aspect of the physical state of a system.

Thanks for the clarification. I was using flow as a metaphore for the transfer of energy to an active state from a more active state. I guess energy would have been a more acurate noun than temperature. Thanks again.

Wow! This is a tricky question . . . The surface of the sun is around 6000 C, but some flares have been measured to be around a million degrees. Granted, it would take a high powered telescope with a huge objective lense to capture the energy of a solar flare and focus it on a spot to even come close to a temperature higher than the surface of the sun, given distance, losses, etc., but it seems (feels???) like it would be theoretically possible.

Now I'm wondering whether or not such a thing can be done with a simple lens . . .

Reply to Bill (483) on Wednesday May 17, @11:36AM (#4952)

That's a good point, but I think these temperatures are in the corona (ionised gas surrounding the sun) rather than solar flares (tho I could be wrong). I did see an explanation once about how it got to temperature way above sun's surface, but I've forgotten what it was, and only thing that comes to mind is charged particles interacting with sun's magnetic field and absorbing energy. Any other ideas out there?

But I doubt whether this could be used to produce high temp on earth. For one thing, the vast bulk of energy reaching earth is from the sun's surface, not the corona.

A magnifying glass has too many limitations to produce the desired effect. Focussing on the most obvious, the problem is that it produces not a point of light from the sun, but an image of finite size of the sun. Further, the index of refraction is a function of wave length so that the image is not planar. Thus the heat from the light incident on the area of the lens will be concentrated not at a point, but over a volume of space. You will never get a small enough image from the spherically ground lens of a magnifying glass. If you go to a system of lenses to counteract this problem, you may gain a lot, but you loose some energy in surface reflection and so forth. Even so, you are no longer using a magnifying glass which is one of the limiting premises of the wager.

I had a hard time picturing this at first. If you take heat from a very large area and concentrate all that energy onto a small area then surely you can make it as hot as you can make it small. What will actually happen is that a magnifying glass works both ways and if the object became hotter than the sun then it would heat up the sun insead of the other way around. -SteveJ

If you had a large enough lens, in orbit, you could heat a piece of earth's atmosphere sufficiently to cause a thunderstorm, then all you need do is induce a lightning strike on your hand, the temperature in a bolt of lightning being hotter than the sun's surface

The maximum temperature you can reach is determined by the wavelength of the light. The lense doesn't change the wavelength of the light, and so it doesn't change the maximum temperature. The sun doesn't output just one wavelength however. The temperature of 6000 degrees is a blackbody equivalent. The sun emits light from deep infared to extreme ultraviolet. So I have to wonder if you had a large lense that gathered just the extreme ultraviolt if you couldn't exceed 6000 degrees at the focal point.

The answer is yes you can do this - in a theoretical sense - that is if you're doing this in a vacuum (pref in orbit) and your target can take the heat. A black body will absorb ALL frequencies of light and then radiate them back out according to Planck's law - that's the whole point of a color temperature. It has nothing to do with absorption, only emission. Here's the problem. If you have an object at the surface of the sun, it is at ~6000K. It sees "sun" over half of its sky. We see "sun" over 1/2 of a degree. Basically you have to reverse the 1/r^2 distance ratio. There is no theoretical limit on making a parabolic mirror that can do that. (A simple lens, because of diffraction effects will probably never work in this application, but the question is more fundamental IMO.) Diffraction limitation is not an issue either. When all else fails, run the numbers: (Source: Wikipedia) Sun: Power 3.83E+26 W Surface Area 6.09E+18 m^2 Energy Flux 6.28E+07 W/m^2 At Earth Radius: Earth Orbit 1.50E+11 m Effective Surface Area at Earth 2.81E+23 m^2 Solar energy @ Earth 1,361 W/m^2 Stefan-Boltzmann Constant: 5.67E-08 W/(m^2*K^4) Effective BB Temp of raw exposure (orbit) 394 K 1mm sphere Surface Area 1.25664E-05 m^2 Power needed to achieve Solar flux 790 W Area of required mirror 0.580 m^2 Diameter (approx - assuming flat) 0.860 m (Folks - you're the engineers, I'm the industry analyst. Next time, don't sleep through physics.)

Exactly!

The sun radiates light at the rate of about 63 million Watts per square meter. Sunlight is received at the Earth at 1370 Watts/square meter. A 5 square meter lens that focused that light to one square centimeter would focus the light to about 64 million Watts per square meter, which is hotter than the sun.

This violates the second law of thermodynamics. Not the spirit of the law, but the letter of the law. This arrangement actually increases the Entropy of the system. The second law seems to work for conduction but not radiation.

EricStruble@Gmail.com

Wouldn't this be similar to the solar furnace used to generate power? For example, there is one in Odellio, France, which is used for scientific experiments - it can achieve temperatures up to 33,000 degrees Celius. Granted, it uses a huge array of mirrors to concentrate the sun's energy instead of a huge lens, but the concept and end result would be similar.

Why not?! And it shouldn't have to be too huge, just precise. Lets just look at the white light through the same lens. Can the focal point be brighter than the light source. I think the answer is yes. This has nothing to do with heat conduction formulas because the sun is seperated from the Earth by a vacuum. An aside; people carrying the fresnel leses from big screen TV's sometimes cut lines in the ground. My guess is, hypothetically, if a one sqare foot lens focused to a square quarter inch produced a 100C rise in temperature, then a 60 sq. ft. lense focused to the same point would produce a 6,000C rise. We are talking about a lens less than 9 feet in diameter, hypothetically. That is assuming the 100C rise, but you get the idea. -Happy