That page only refers to the two lens astronomical telescope which I have already accepted. It does not refer or prove anything in more general terms.
The complexity of the optical system doesn’t matter. In the end, you’ll have an effective increase of zero. Magnitude and Magnification are intrinsically and proportionately tied together. No getting around this using pure optics. At all.
That’s all I can say as a layman, myself.
Well, that is just an affirmation, not a proof. I have seen camera lenses which at first sight seemed impossible and yet they existed. I just didn’t understand them.
Again, the fact that I have never seen it is a strong indicator that it probably does not exist. If it does not exist this would be a strong indicator that it cannot be done because I would think it would be useful for military and civilian purposes. So, I am inclined to think that it is highly probable that it is not possible. But this is not proof, it is conjecture.
Here is another conjecture: if the proof exists it is relatively simple, probably in the form of geometric proof, not complex and mathematical.
In general terms, any passive system that could magnify the intensity of light would violate the second law of thermodynamics. It would allow you to start with a system at a uniform temperature, which will have the black body spectrum, and concentrate more energy of that spectrum at some location. That location would then heat up, and the system would no longer be in equilibrium.
It does not have to amplify what it collects, it just has to collect more of it.
A convex lens or mirror catches the rays of the sun and concentrates all their energy in one point, for example a turnip. That turnip is getting a lot more energy than if it were just put out there in the sunlight with no optical system.
I get where you’re coming from. Really. But in this case where what yourself and the OP are describing would be creating, essentially, a perpetual source of energy that violates the laws of thermodynamics.
As ZenBeam points out, you can’t get more energy out of a passive system than you put in. The intrinsic amount of radiation hitting your eye/telescope/binoculars/futuristic apparatus is the threshold of energy for the system. You spread thin that energy in magnifying the angular dimensions in apparent size, so you lose in magnitude (heat and light) what you gain in size/resolve. Vice versa for reduction, you gain magnitude (heat and light) for loss of apparent size and resolve.
Therefore, it follows, you cannot increase the intrinsic energy of radiation entering your device at a 1:1 ratio of magnitude/magnification without using some method to pump more energy in. Hence then invention of cameras with long exposures, or CCDs that can increase the gain, etc.
The proof is in the astronomically sound laws of electro and thermodynamics.
For the sake of speculation, lets assume first that you aren’t looking at a point source of light but maybe an evenly lit room; in any particular direction there is no bright spot or dark spot, no light bulb or shadow. If your eye is the detector, the limiting aperture is the pupil of your eye. Opening the pupil will allow more light into the eye, the room will appear brighter. However, there is no optical element that can be placed in front of or around the eye that will “amplify” a photon passively so that one photon hits and more than one is emitted to then be received by the eye. Photons have quantized energy, you want brighter, you need more. A lens of any kind will diffract a light beam (and reflect some, too), allowing more light to be transmitted to your eye by increasing your field of view (if that is the purpose of the lens).
This is because you’re doing the inverse of magnification (reduction), and focusing a very tiny image of the sun (and with it, it’s intrinsic light and heat) into a very small area on the turnip, that’s otherwise diffuse and unfocused so it’s only getting a small fraction of the sun’s light.
How are you collecting more of it, and concentrating it into a smaller area, without increasing its intensity?
If you’re in the middle of the Sun, you’re already getting energy from all directions. A magnifying glass or mirror won’t help.
You have totally lost me but I just want to assure everyone I am not in the middle of the sun nor do I have any intention of going there or using any devices there in the near future. I think this may be getting too strange for me.
ZenBeam’s first post in this thread is 100% correct, and applies to any passive optical system of arbitrary complexity. As many others have stated, a passive optical system which increased the brightness in any sense but which did not magnify the image would violate the first and/or second laws of thermodynamics.
In essence, as the saying goes, this is not an engineering problem, but a law of physics restriction; that is, if you put any stock into our current laws of thermodynamics.
In optics, it’s easy to forget that with light, comes heat, in a word, energy. This is your threshold, or ceiling, of what’s possible in intensity through passive optics. As you magnify something using passive optics, the energy of the radiation will dilute or concentrate across a surface it’s projected on if magnified or reduced in apparent size respectively (by the inverse square I believe: 2x larger, 4x dimmer; 3x larger, 9x dimmer, 4x larger, 16 times dimmer, etc.)
The opposite of the above for using a concave mirror to focus the entirety of the sun’s heat and light onto a tiny area of a turnip.
In post 64, I posited a system at uniform temperature. The whole system at one uniform temperature. When you talk about using a magnifying glass to heat up a turnip, that only works because you are not in a system with uniform temperature everywhere. A magnifying glass or mirror, in a system at a uniform temperature, won’t change the amount of energy your turnip receives.
You didn’t answer my question from my last post, so i’ll repeat it:
How are you collecting more of it, and concentrating it into a smaller area, without increasing its intensity?
I dunno, but let’s try it on Vinyl Turnip. We can finally see what he’s really made of.
That’s kind of the whole point, to increase its intensity. There’s nothing about this that violates the law of conservation of energy. If you could take the light hitting a 200mm primary and focus it all through a 7mm lens without magnifying the image, the surface brightness would necessarily be (200/7)^2 as bright minus any light that got reflected back or absorbed or else there is a violation. Now whether it can be done without magnifying the image is the question, and I’m reasonably sure it can’t with a simple reflector or refractor telescope with a plossl eyepiece because the eye relief seems to be inversely proportional to the magnification, but no one has managed to describe how there are eyepieces that increase the eye relief at a certain magnification and why that can’t work in reverse.
It simply comes down to the inverse square law of light, as to why magnification will be at or >100% in intensity to that of the naked eye, and reduction will be at or <100% to that of the naked eye.
This wouldn’t violate conservation of energy, but it would let you violate the second law of thermodynamics. See post 64.
This is a very elegant way of proving you are right. Nevertheless, I am interested in an explanation of why this not possible in terms of optics.
Like snailboy, I don’t see why you can’t have a large objective lens, with a larger surface area than your eye, which collects significantly more photons (due to the larger surface area) and then focuses them down into a 7mm exit pupil, producing an image at 1:1 magnification but significantly brighter.
Unfortunately, like other fundamental laws of physics, this one is hard to answer aside from “that’s just the way it is”. I’m sure you’ve seen that there are an infinite number of perpetual motion machines out there. Each one obviously violates conservation of energy. But some of them are very clever and only fail due to some very small detail. It seems that the universe conspires against us in violating its rules.
That said, I think I can answer your specific question (hopefully someone else can confirm). Even though your objective appears to be collecting a bunch of photons due to its large surface area, it really isn’t. The reason is that the lens has a reduced acceptance angle as compared to what you would see with your eye. Photons arrive over a larger area, but there is a proportionally smaller solid angle over which they will refract correctly to arrive at your eye. The flux ends up coming out equal.
This is an interesting question, and thinking about it, nothing leapt out at me as a way of showing it within the context of geometrical optics. But I went looking through the optics pages at Wikipedia, and it looks like the explanation is in terms of etendue.
Yeah, I never heard of it before today either, so I’ll just let you read the page. The section on Maximum Concentration in particular seems to directly address your question. ETA: That section’s picture and equations go nicely with Dr. Strangelove’s last paragraph in the previous post.