Comment All about the focal ratio (Score 1) 584
It may be too late in this discussion to explain the difference between the Mythbusters and the MIT experiments, but...
Basic thermo applied to optics means that no purely optical system can increase the surface brightness of an extended object. Old important optics theorem. Check any introductory textbook for the proof.
What this means is that, from the target's point of view, no part of the lens/mirror/whatever system is going to be any brighter or hotter or provide more energy per square degree than the sun does. Instead, the mirrors or lenses or whatnot only make it seem as if, from the targer's point of view, there are more suns covering more of the field of view.
Therefore, the limiting factors in the temperature the target will reach are the size of the optical system and how far away it is. If it's small enough or far enough that it appears, to the target, about the same size as the sun in the sky, it will provide about as much energy as the sun does, and the target temperature should roughly double. The weapon can't do any more, because it can't be any brighter than the sun itself.
On the other hand, a strong magnifying glass held near a twig covers at least half the sky from the twig's prospective, and all that area can provide as many watts per square degree as the surface of the sun. The sun, taking up something like a ten-thousandth of our sky, provides almost all the heat energy that keeps us and our planet alive. It's not hard to imagine what happens when, from a specific prospective, it suddenly seems to cover a tenth, or a half. Nearly-instant campfire. Or fried eyeball if the prospective happens to be yours.
This in mind, a quick look at the experimental setups from Mythbusters and MIT explains the difference in their results. The TV crew used a moderate sized cluster of mirrors at some distance from the target. Probably covered a few square degrees, or 8 or so sun areas. The collection of MIT students was fairly large and quite a bit closer, and covered far, far more of the target's 'sky' with sun image. It's no surprise that their target got quite a bit hotter. Personally, I'm not at all convinced that the MIT scheme could have been used during an actual battle. To duplicate their results would have required that either the soldiers move very close, or that they have a very large number of them.
For anyone who's interested, this ratio between the size, or _aperture_, of an optical system and the distance at which it brings light to a focus (the _focal_length_) is a common parameter used to describe the system known as the focal ratio or f-number. This is why two camera lenses of the same focal lengths but different f-numbers will require different exposure times to properly expose a piece of film or a CCD sensor.
And yes, for those who've checked, this explanation does directly contradict the FAQ from the MIT experiment's site. The professor argues that the distance isn't relevant to the results they got, because the light energy from their mirror system can be focused arbitrarily tight. That would be the case only if the sun was a point source rather than an extended object. If they had actually tried the experiment at more realistic distances they would have found that their mirrors projected images of the sun on the ship that were too large and blurred to heat it much, unless they added more students with mirrors to fill up more aperture and compensate.
The MIT class appears to have been an introduction prototyping and product validation. It intrigues me that, by misunderstanding the underlying theory, they ended up modifying a parameter that was actually crucial to their results and validating a scheme that would be, at best, cumbersome in the real world. What this implies for the design and test process is, ah, left as an exercise for the student.
Basic thermo applied to optics means that no purely optical system can increase the surface brightness of an extended object. Old important optics theorem. Check any introductory textbook for the proof.
What this means is that, from the target's point of view, no part of the lens/mirror/whatever system is going to be any brighter or hotter or provide more energy per square degree than the sun does. Instead, the mirrors or lenses or whatnot only make it seem as if, from the targer's point of view, there are more suns covering more of the field of view.
Therefore, the limiting factors in the temperature the target will reach are the size of the optical system and how far away it is. If it's small enough or far enough that it appears, to the target, about the same size as the sun in the sky, it will provide about as much energy as the sun does, and the target temperature should roughly double. The weapon can't do any more, because it can't be any brighter than the sun itself.
On the other hand, a strong magnifying glass held near a twig covers at least half the sky from the twig's prospective, and all that area can provide as many watts per square degree as the surface of the sun. The sun, taking up something like a ten-thousandth of our sky, provides almost all the heat energy that keeps us and our planet alive. It's not hard to imagine what happens when, from a specific prospective, it suddenly seems to cover a tenth, or a half. Nearly-instant campfire. Or fried eyeball if the prospective happens to be yours.
This in mind, a quick look at the experimental setups from Mythbusters and MIT explains the difference in their results. The TV crew used a moderate sized cluster of mirrors at some distance from the target. Probably covered a few square degrees, or 8 or so sun areas. The collection of MIT students was fairly large and quite a bit closer, and covered far, far more of the target's 'sky' with sun image. It's no surprise that their target got quite a bit hotter. Personally, I'm not at all convinced that the MIT scheme could have been used during an actual battle. To duplicate their results would have required that either the soldiers move very close, or that they have a very large number of them.
For anyone who's interested, this ratio between the size, or _aperture_, of an optical system and the distance at which it brings light to a focus (the _focal_length_) is a common parameter used to describe the system known as the focal ratio or f-number. This is why two camera lenses of the same focal lengths but different f-numbers will require different exposure times to properly expose a piece of film or a CCD sensor.
And yes, for those who've checked, this explanation does directly contradict the FAQ from the MIT experiment's site. The professor argues that the distance isn't relevant to the results they got, because the light energy from their mirror system can be focused arbitrarily tight. That would be the case only if the sun was a point source rather than an extended object. If they had actually tried the experiment at more realistic distances they would have found that their mirrors projected images of the sun on the ship that were too large and blurred to heat it much, unless they added more students with mirrors to fill up more aperture and compensate.
The MIT class appears to have been an introduction prototyping and product validation. It intrigues me that, by misunderstanding the underlying theory, they ended up modifying a parameter that was actually crucial to their results and validating a scheme that would be, at best, cumbersome in the real world. What this implies for the design and test process is, ah, left as an exercise for the student.
