# Light beam reduction

#### GeorgeSol

I've been wondering if it is possible for a large aperture lens, or mirror, to receive parallel rays of light, converge them, then diverge them into a smaller beam of parallel rays as they exited the optical device?

If so, directing this greater flux density into a telescope matching the beam's diameter should increase the apparent surface brightness of an extended celestial object, a non-point source (e.g. star). This would improve imaging exposure times and allow for the design of a telescope which one could see celestial objects in color - a colorscope.

Improving surface brightness of extended objects is supposedly a violation of the 2nd law, but I don't see it.

Any ideas?

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#### Kurdt

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Gold Member
Well a device that takes parrallel rays and condenses them into a smaller parallel beam is a telescope. Are you attempting to stack telescopes in an attempt to get a better image?

#### GeorgeSol

Normal telescopes, as far as I know, do not produce parallel rays. They focus light which allows an object to appear magnified, or enlarged on a sensor.

However, if a pre-scope could be added that would create parallel rays, I would expect objects would appear brighter, but would have less magnification.

The optical equations which deal with these indicate you can not achieve it. Consider the following....

Exit Pupil = Aperture/ Magnification

The exit pupil is the diameter of the cone of light exiting the telescope. The eye has an "entrance pupil" of between 5mm to 7mm, depending on age, etc., in darkened conditions (2mm to 3mm for daytime). Therefore, scopes and binoculars, are designed to get most of the light into the eye by limiting the exit pupil.

My hope is that the above equation is a design equation and not one physics has cast in stone.

If parallel rays exit the scope, they would offer no magnification. A magnification of one, per the equation, would mean the exit pupil diameter would equal the aperture of the scope. A 12 inch aperture telescope with parallel ray output would produce an exit pupil of 12 inches. Nothing would be gained, if this equation is mandated by physics.

It just seems to me that some optical arrangement would easily allow an output of parallel rays of less diameter.

I don't see the Zeroth law preventing it as their is no gain in "temperature" over the objects, only increased flux density. I also don't see how the 2nd law would prevent it.

The 2nd law would be an issue if the claim was to increase surface brightness at little to no loss in magnification. There are only so many photons to play with, afterall. :)

Astronomers say it can't be done and will site the 2nd law but fail to explain why, at least so far.

#### Kurdt

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Gold Member
The eye piece magnifies a telescope image. The telescope itself produces a parallel beam. In effect what you are suggesting is just the same as making a single telescope with a mirror or lens the size of the of your pre-scope.

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#### Kurdt

Staff Emeritus
Gold Member
For example look at the ray diagram of a refracting telescope near the bottom of the page on the following web page.

http://www.antonine-education.co.uk/Physics_A2/Options/Module_5A/Topic_1/topic_1_lenses_and__refracting_t.htm [Broken]

I hope this makes things clearer.

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#### GeorgeSol

Kurdt said:
The eye piece focuses a telescope image. The telescope itself produces a parallel beam. In effect what you are suggesting is just the same as making a single telescope with a mirror or lens the size of the of your pre-scope.
Yes, you're right. What was I thinking? Apparently, without the eyepiece, they aren't parallel, but what's a telescope without an eyepiece.

However, increasing the aperture would, according to the equation, increase the exit pupil. Surprisingly, this will not increase the apparent surface brightness of celestial objects. An 8 meter telescope does not improve the surface brightness as would be seen by the naked eye, but does magnifiy it signicantly.

Yet, using the pre-scope idea for illustration only, greater flux density would seem to occur, and should cause an object's surface brightness to increase. Is this likely? What am I missing?

#### Kurdt

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I haven't worked with telescopes in a while so apologies for that eyepiece stuff but you got what I was getting at so thats alright. Really your idea about the pre-scope gathering more light and making things brighter is exactly how telescopes work now. The reason we can see some stars with telescopes and binoculars that we can't see with the naked eye is because they have gathered light over a larger area and concentrated it into something that we can see. If you want to observe fainter objects you generally make a larger objective lens or mirror to cover a wider area. You pre-scope idea would work but its not practical because you have twice the amount of optics and as I hope you know optics is an expensive business. Unfortunately the idea is unnecessary.

#### GeorgeSol

Kurdt said:
I haven't worked with telescopes in a while so apologies for that eyepiece stuff but you got what I was getting at so thats alright.
I should point out I haven't worked with their design at all. I have thought about buying optical design software to try different ideas, but I have a lot on my plate already.

Really your idea about the pre-scope gathering more light and making things brighter is exactly how telescopes work now. The reason we can see some stars with telescopes and binoculars that we can't see with the naked eye is because they have gathered light over a larger area and concentrated it into something that we can see.
Yes, but that is for stars which do not increase in size (ie magnification). Larger aperture will, of course, gather more light but for "extened objects", e.g. nebula, this light is spread out due to the magnification. Albeit, your eye will be able to see extended objects appear as if they were somewhat brighter due to physiological reasons, which I don't really understand much. But the light flux per unit area of an extended object, with the aid of a telescope, on your retina, or on a sensor, will be less than the flux per unit area on your unaided retina. The rule is...you can not increase this flux density. But, I ask....why not?

If you want to observe fainter objects you generally make a larger objective lens or mirror to cover a wider area. You pre-scope idea would work but its not practical because you have twice the amount of optics and as I hope you know optics is an expensive business.
If we can establish a double telescope, or other impractical contraption :), will increase surface brightness, then the optical experts can take it from there. If not, I'll do it myself. First, I have to know if it can be done using any gedankenexperiment. :)

#### Kurdt

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I don't see any reasaon why your setup should not work if you want to make it.

#### GeorgeSol

Odd, you're suppose to!

It's suppose to be a violation of the 2nd law, or some radiation law. How's your thermo? Mine is rusty, but what little I recall, I just don't see why it would be a problem either. I tried bautforum.com but the answer was not resolved there either.

I had a little correspondence with a professional in optical accessories. He revealed that a telecompressor can improve surface brightness by as much as 44x, but, apparently, only when the exit pupil is so large it requires this much reconcentration. He indicated that we can not increase surface brightness beyond that of the naked eye, but offered no infomration why this was his view.

"Why not" is still the question?

One weak explanation as to why it is not done, assuming it could be, is due to the purpose of the scope for the amount of money invested -magnification is too important to sacrifice for surface brightness. Most astronomy is not visual, thus longer exposure times will indirectly raise the surface brightness of any object. However, recently, more very fast exposure times with subequent image stacking provides superior resolution. One amateur, using a small telescope (10 or 12 inch I think), recently imaged Jupiter and its moons that showed surface features on Ganymede!

If this is the case, it is time to rethink using today's lower cost large apertures to improve surface brightness and reduce exposure times. [Also, there is still that desire I have to see objects in full color. ]

Do you know where else I could go for help?

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#### Kurdt

Staff Emeritus
Gold Member
Well I'll have a proper look into it if you wish and see if I can find any explaination. Like I say I'm more into general relativity and quantum mechanics at the minute so I might have to re-educate myself on a few things since its been a while since I've dealt with them. If you can find out what specific 2nd law you're alluding to aswell that would help. if I remember correctly the second law of thermodynamics relates to heat engines or something so I doubt its a thermo law. Most likely a black body radiation one. As for other sources, I frankly have no idea. You could try contacting some professionals more into optics or if they have an optics forum somewhere they might know better than me. Where to find an optics forum? I do not know.

I'm fairly busy but you have grabbed my interest so when I get any spare seconds I'll do some research. Good luck though if you head off anywhere else.

#### GeorgeSol

Kurdt said:
Well I'll have a proper look into it if you wish and see if I can find any explaination.
Great if you can, or direct me somewhere.

Like I say I'm more into general relativity and quantum mechanics at the minute.
Hmmmm...the photoelectric effect has popped into my head a time or two about this topic. We can't increase the energy but there is no reason why we can't concentrate the volume. I see no qm issue with this idea, but, admittedly, I know very little of qm.

If you can find out what specific 2nd law you're alluding to aswell that would help. if I remember correctly the second law of thermodynamics relates to heat engines or something so I doubt its a thermo law.
It applies to all energy exchange. My favorite definition is...."heat won't flow from a cooler to a hotter, you can try if you like, but you far better notter".

The claim against surface brightening appears to stem around this idea that light can't be concentrated more than it is (perhaps in the focal plane only).

Where to find an optics forum? I do not know.
Yes, there are some but they're pretty inactive.

I'm fairly busy but you have grabbed my interest so when I get any spare seconds I'll do some research. Good luck though if you head off anywhere else.
Thanks.

Perhaps another physicist is in the house, also. [hint]

#### cesiumfrog

GeorgeSol said:
Improving surface brightness of extended objects is supposedly a violation of the 2nd law, but I don't see it.
This has to do with Liouville's theorem, conservation of phase space volume; I'm not sure whether it relates to entropy. I'll try to post something intuitive regarding surface brightness later, or you could google some astronomy info.

#### Labguy

GeorgeSol said:
Exit Pupil = Aperture/ Magnification

The exit pupil is the diameter of the cone of light exiting the telescope. The eye has an "entrance pupil" of between 5mm to 7mm, depending on age, etc., in darkened conditions (2mm to 3mm for daytime). Therefore, scopes and binoculars, are designed to get most of the light into the eye by limiting the exit pupil.
Some of the posts above are at least 20% correct and the rest are ridiculous. Looking for any laws of thermodynamics to figure a "pre-telescope" is a dead end.

Your first quoted line above is correct, but "The exit pupil is the diameter of the cone of light exiting the telescope" is totally incorrect. In any telescope, the diameter (aperture) of the light entering the scope (or any optical instrument) is the entrance pupil, not exit pupil. The objective (lens or mirror) does not produce parallel rays, it forms a "virtual image" at the focal plane where it takes a device of some type to form an image. For visual, this would be an eyepiece as Kurdt mentioned somewhere above. It is the eyepiece that makes the large amount of focused (conical) light turn back into a parallel smaller bundle of light, the exit pupil. Then, your eye takes in the parallel light from a large beam (entrance pupil) that has been converted to a small beam (exit pupil). The smaller the exit pupil (different eyepieces) the greater the magnification.

Brightness and image size,of extended objects, depend on just focal length and magnification. More magnification = less surface brightness.

From an earlier post a long time ago:
Labguy said:
First, a telescope twice as big gathers four times as much light; everyone agrees. But, "four times brighter" can be true in some instances, but 4-times brighter does not mean four magnitudes. The magnitude system is an arbitrary system agreed on in the late 1800's by astronomers to standardize the system all were using with their old photometers to measure brightness back then. They settled on a system where a difference of 5 magnitudes would be "exactly" a difference in brightness of 100 times. So, one magnitude equals the 1/5th root of 100, which is about 2.5119. Most just use 2.512; close enough.

So, a difference in objects of one magnitude means the brighter one is 2.5119 times brighter than the other. A difference of 2 magnitudes = a difference of 6.310 times in brightness. Four magnitudes is a difference of 39.811 in brightness, so you can see that brightness as perceived by the eye actually has nothing to do with the magnitude system unless you just happen to want to be able to translate the two; eye to magnitude or, more likely, photometer to magnitude.

As for telescopes and brightness (perceived by the eye) a whole lot of factors come into play, too many to list here except the main ones. Brightness, to the eye, depends on what is usually called the exit pupil delivered by the telescope. The exit pupil (EP) is usually expressed in millimeters and is just the entrance pupil of the telescope (diameter) divided by the power of the particular eyepiece being used. Turn the math around and exit pupil just becomes the focal length of the eyepiece (in mm) divided by the f/ratio of the telescope's objective (lens or mirror). So, the "brightness" of an object will only be four times brighter in the twice-as big telescope if the same focal length eyepiece is used in both scopes and both scopes have the same focal length. It is safe to equate exit pupil with "brightness". Just think of the exit pupil as being the diameter of the "beam of illumination" coming out of the telescope / eyepiece being used, because that's exactly what it is!

Example 1:

8", f/3 scope (24" focal length) with a 15mm eyepiece has exit pupil of 5.0mm. (15mm eyepiece divided by 3).

4", f/6 scope (24" focal length) with a 15mm eyepiece has exit pupil of 2.5mm. (15mm eyepiece divided by 6).

So here, the 8" scope is twice as bright as the 4" scope (5.0 vs. 2.5). Also note both will show the same "power" of about 40.6X, since power is just the focal length of the objective divided by the focal length of the eyepiece. (inches were converted to millimeters)

Example 2: (Clone 4" scope to twice the size)

8", f/6 scope (48" focal length) with a 15mm eyepiece has exit pupil of 2.5mm. (15mm eyepiece divided by 6).

4", f/6 scope (24" focal length) with a 15mm eyepiece has exit pupil of 2.5mm. (15mm eyepiece divided by 6).

Here, both scopes have the same exit pupil so the 8" scope is not twice as "bright", it is the same at 2.5mm exit pupil. But, do the division and notice that the 8" scope now gives twice the power of the 4" scope; that's the trade-off between "power vs. brightness". Go to: this site and enter any scope / eyepiece combo to see what you get; it's fun.

As for the human eye, there are limiting factors for sure. The 1cm (10mm) eye quoted above is a bit off. The largest most any eye will dilate in total darkness is about 7mm. But, this is very rare and is limited to very young people and only if fully "dark-adapted". Getting dark adapted doesn't just mean being in a dark place for awhile, it takes total darkness with no other light source around to ruin it. Also, the maximum an eye will dilate decreases, in everyone, with age, and anyone over about 25 will start to lose the ability to dilate to 7mm. Most people over about 40 can't even get to 5mm. On a sunny day our eyes are only dilated to about 2mm to 2.5mm. If we only have a 2.5mm eye opening, there is no sense (reason) to use something (binoculars for instance) that gives an exit pupil (light-beam diameter) larger than that since all the light can't enter the eye anyway. This is why, in daylight, 7X50 binoculars (~7mm EP) will not make things seem any brighter than 7X35 binoculars (5mm EP). With telescopes, reasonable EP's to use will range from about 5.0mm (bright, low power) down to ~ 0.8mm (dimmer, high power). The upper limit is a limit based on our eyes and the lower limit is a limit based on the telescope's abilities. It takes a very dark sky location and great "seeing conditions" (atmosphere) to push a scope's power to anything that gives a smaller EP than about 0.8mm.
and:
Labguy said:
I = ((A)(F)(25.4))/57.3

Where:
I = Image size in mm.
A = Angular size of object in degrees. *
F = Focal length of objective in inches.

* For (A) in arc minutes: Divide by 3438 instead of 57.3
* For (A) in arc seconds: Divide by 206280.

Image size is a function of focal length only. The result of the formula above will be the image size for any type of telescope or lens / projection system of known effective focal length. It applies to an image on film, CCD, or any type of detection device. This, of course, excludes stars where the image would always be seen as a "point source". An increase in aperture will not increase the image size without an increase in focal length; it will only increase the f/ratio making photo or CCD exposure times shorter for the same image "brightness". An aperture increase will, obviously, also increase the potential resolution.
All of this has been hashed before,so do a search and find the old thread.

#### GeorgeSol

cesiumfrog said:
This has to do with Liouville's theorem, conservation of phase space volume; I'm not sure whether it relates to entropy. I'll try to post something intuitive regarding surface brightness later, or you could google some astronomy info.
That would be most appreciated.

labguy said:
Some of the posts above are at least 20% correct and the rest are ridiculous.
Try to look past the grammar and address the issue. At least 40% is correct.

Looking for any laws of thermodynamics to figure a "pre-telescope" is a dead end.
The pre-telescope idea is an illustratitive tool to emphasize improvement to flux density. Improving the flux density onto the retina, or sensor, without change in magnification should improve surface brightness. Is this not correct?

Your first quoted line above is correct, but "The exit pupil is the diameter of the cone of light exiting the telescope" is totally incorrect. In any telescope, the diameter (aperture) of the light entering the scope (or any optical instrument) is the entrance pupil, not exit pupil.
The bold emphasis may help see your error. However, I did not mean to say the exiting light was conical, but I thought it would pass inspection.

I had not seen the term entrance pupil applied to the light entering a telescope. Is this a common use?

The smaller the exit pupil (different eyepieces) the greater the magnification.
Good point. However, a telecompressor will reduce the exit pupil without increasing the magnfication. So, optics have power over this rule. It is this kind of thing that I am trying to learn; which rules can be broken, and which can't?

Brightness and image size,of extended objects, depend on just focal length and magnification. More magnification = less surface brightness.
Yes, of course, since we only have a fixed amount of flux. Yet, what if we, somehow, could increase the flux for any given exit pupil? This would increase the surface brightness. But, how this can be done is my quest.

Your quote from another thread covers a lot of nice information concisely, yet none of it directly helps this issue of surface brightness, however. I tried searching but have failed. Is there a thread which shows searching terms?

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#### Labguy

Try to look past the grammar and address the issue. At least 40% is correct.

Ok, I'll concede that.

The pre-telescope idea is an illustratitive tool to emphasize improvement to flux density. Improving the flux density onto the retina, or sensor, without change in magnification should improve surface brightness. Is this not correct?

Yes, but all you need to do for that is increase the aperture of the telescope and use an eyepiece that will keep the same magnification as in the original, smaller scope. BUT, that will also increase the exit pupil which can soon become too large to enter the eye, as described in one of my "brightness examples" in my last post. It will also change the size of the "virtual image" falling on any type sensor where it would likely become larger than the sensor 's detection area.

The bold emphasis may help see your error. However, I did not mean to say the exiting light was conical, but I thought it would pass inspection.

Yes, the entrance pupil is the light entering the scope, the exit pupil is the beam diameter leaving the scope/eyepiece combination. My answer was correct, but your post said: "The exit pupil is the diameter of the cone of light exiting the telescope" which is not correct. It (exit pupil) is not a cone.

I had not seen the term entrance pupil applied to the light entering a telescope. Is this a common use?

Yes it is. Exit pupil can be figured by (1) the entrance pupil/magnification OR by turning the math around where it equals (2) (Eyepiece focal length / telescope f-ratio)

Good point. However, a telecompressor will reduce the exit pupil without increasing the magnfication. So, optics have power over this rule. It is this kind of thing that I am trying to learn; which rules can be broken, and which can't?

A telecompressor will shorten the effective focal length (EFL) of a scope and a teleconverter (Barlow lens) will lengthen the EFL. Either one of these will change both the image scale AND the power of any given eyepiece.

Yes, of course, since we only have a fixed amount of flux. Yet, what if we, somehow, could increase the flux for any given exit pupil? This would increase the surface brightness. But, how this can be done is my quest.

As above, no way to do it except increase the aperture. It will increase image scale and/or magnification, but the "flux" will remain a constant total

Your quote from another thread covers a lot of nice information concisely, yet none of it directly helps this issue of surface brightness, however. I tried searching but have failed. Is there a thread which shows searching terms?

The brightest you will ever see "surface brightness" is with your unaided eye. Period. BUT, the image scale is so small that you can't resolve any detail in any object with a small angular distension. A telescope will get you more magnification to see detail, but every increase in power will result in less surface brightness. That has and will always be the trade-off between brightness and power. That was also explained in one of the "telescope brightness" items I posted before. Think about it, an object like the Crab Nebula only emits a finite number of photons. If you increase the image scale (with a telescope) you spread the same number of photons over a larger apparent area, so the surface brightness will be decreased.

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#### cesiumfrog

What is surface brightness? A measure of the power (energy per unit observation time) received from some source, per unit area of instrument aperture, per unit (solid-) angle of the source. (Note that the power received from a source can be determined by that source's total luminosity together with what fraction of the source's sky that is subtended by the receiver aperture's area.)

Now for the Liouville theorem: volume in phase space stays constant. Imagine the light beam from a torch: Close to the torch the beam has a narrow cross-sectional area and, at each point there, there are photons travelling in a wide range of directions. Much further from the torch the beam has a far wider cross-sectional area but the rays there are almost parallel (there is a proportionally narrow range of photon momenta at any such point). Even if you try (say, using some lenses) to reduce part of the beam onto a smaller area, the photons that reach any given point in this smal area are again moving in a wide range of directions.

$$B_{Surface} = \frac P {\Omega\ A_{aperture}} = \frac{L \frac \Theta {4\pi}}{\Omega\ A_{{ap.}}} = \frac{L ({\frac{A_{ap.}}{A_{total}}})}{\Omega\ A_{ap.}} = \frac{L_{source}}{(\Omega\ A_{total})_{Liouville}} = \frac{L_{source}}{({(2\pi)(4 \pi R_{source}^2)})}$$
$$\Omega$$ is subtended by source, at observer. (Also describes range of photon momentum there.)
$$\Theta$$ subtended by aperture, at source.

Geodesics in GRT are just one application of Liouville's theorem. The above equation is missing various factors of redshift (since time, energy and area become subjective) but should illustrate the idea that surface brightness is a constant of the source.

The relation to entropy http://www.av8n.com/physics/phase-space-thin-lens.htm" [Broken]has to do with how small an area you can focus light onto.. and hence, whether you can use sunlight to heat something above the temperature of the sun.

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#### Labguy

Years later I learned about Liouville’s theorem, and realized that no such system is possible. Each of the deep-sky objects I was interested in is intrinsically so dim that even if you travelled there and stood next to the object, you couldn’t see it with the naked eye. (The beautiful pictures you see come from long time exposures, which the eye cannot do.) No system of lenses (or any other passive system) can produce an image with more surface brightness than the original object.

Which is a clearer way of stating exactly what I was trying to explain in my post above. The link also says:
If I made the aperture bigger at constant focal length, the exit pupil became too big (bigger than 7mm, the diameter of the dark-adapted eye). If I made the exit pupil smaller, it always seemed to come at the cost of more magnification than I wanted, meaning the image was too spread out, i.e. too few photons per unit area per unit time, i.e. too dim.
Which IS exactly as I explained above but with different wording. Thanks for the link.

#### GeorgeSol

cesiumfrog said:
... should illustrate the idea that surface brightness is a constant of the source.
I only marginally grasp the equation, but I think it may show that the suface brightness can not change regardless of whether you move closer or further. If so, it can be shown in a lucid explanation. If you double the distance between you and the object, the amount of from the object will be reduced as the inverse square of the distance traveled. But, the apparent size of the object will also be reduced by the inverse square. Therefore, they will cancel and the same surface brightness will be seen.

However, on second thought, the theorem seems to deal more with the light angle. I learned that if a magnfiying glass was placed in front of an infinitely wide isotropic light source, it would not be able to burn a leaf any faster than without a magnifying glass. [I recently bet an ice cream that a magnifying glass at the sun would burn a leaf faster than without using a magnifying glass. Surprisingly, it will.] Since only the parallel rays into the glass would be concentrated onto the leaf, the other rays will be concentrated elsewhere due to their angle. Moving the glass further from the source will increase the number of parallel rays but fewer photons will arrive. Is this a better explanation of the theorem?

Now take two observers who have adjacent telescopes, if their optics are perfect, and light had no obstructions from an extended object, they will each see the object at the same surface brightness (per unit area). The total flux will be twice that of just one observer. If we could take the flux from one and add it to the other, we would double the surface brightness seen. This, hopefully, is a little different than usuall.

I thought I had a handle on the inability to increase surface brightness by using the zeroth law. Using a magnifying glass to concentrate light onto something, say a leaf, we can realize that the spot can not be hotter or brighter than the source because if it could, then we could reverse the light and produce a hotter source; which, of course, is impossible.

However, once again, if we augment the light from one area onto another, we may be able to produce a brighter image. We would be taken energy, i.e. photons, from one area and routing them onto another.

This works easy enough for mass. My rain gauge has a large opening at the top to increase the normal accumulation of drops in order to amplilfy the volume received. Here, we can see the flux density is increased by the funnel action at the top. We could use numerous examples, of course. The temperature of the water, ignoring the P.E. difference, is not higher, so the 2nd law is fine. Only an increase in flux has been demonstrated. Yet, we can not do it with photons and maintain an image, for some reason.

The relation to entropy http://www.av8n.com/physics/phase-space-thin-lens.htm" [Broken]has to do with how small an area you can focus light onto.. and hence, whether you can use sunlight to heat something above the temperature of the sun.
Ooohh, there she be, apparently. Thanks, that has to be it. [Let me babble a little and see if anything sticks.]

Yet, consider this gedankenexperiment... Let's take mirrors and surround one hemisphere of the sun. All the mirrors will concentrate their reflected light onto one small spot on the surface. Will this not increase the surface temperature at that spot? Albeit, even if we cut a hole in the middle of the mirrors to allow observation of a solar area, unfortunately, I see no way to redirect the light into the path seen by a telescope. As for ideas, I suppose the rain gage holds more water, so to speak.

So, in my limited mind, it still makes sense that if we could combine the light of two scopes of equal aperture, then we could double the brightness. Yet, I can't see how. One would think larger aperture would work, as per the rain gauge model. I still don't grasp why not.

Perhaps, if I understood the dX/dt aspect of phase space, I would see why light is so different to restrict flux concentration.

If we increase photon flux onto an object, will it increase temperature? Maybe this is a good approach.

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#### cesiumfrog

GeorgeSol said:
[Let me babble a little and see if anything sticks.]

Yet, consider this gedankenexperiment... Let's take mirrors and surround one hemisphere of the sun. All the mirrors will concentrate their reflected light onto one small spot on the surface. Will this not increase the surface temperature at that spot?
No it will not. If it did, that spot would heat the rest of the sun further, ad perpetuum. Try sketching the ray diagram.

As for babble, expressing your ideas succinctly promotes sharper thought!

#### GeorgeSol

cesiumfrog said:
No it will not. If it did, that spot would heat the rest of the sun further, ad perpetuum. Try sketching the ray diagram.
The flux from the surface that receives more flux from the mirrors will have to heat-up, right?

I want to say the water wheel was the earliest system that helped get thermo off the ground. Hopefully, this will be analogous. Let's consider one that is 50% efficent and all the power is used to return water....

Fl ~ flow from lake (always 1000 gpm)
Fi ~ flow of input onto the wheel
Fr ~ returned stream of water
F ~ total flow onto the water wheel, (after a delta t)
Fd ~ flow of discharge downstream

Initially,
Fl = Fi = 1000 gpm
Fr = 500 gpm (based on the 50% efficency)
F = 1500 gpm

Then, with an F of 1500 gpm,
Fi = 1500 gpm
Fr = 750 gpm (50% of 1500)
F = 1750 gpm

Eventually, assuming the 50% efficency never varies, the value of F will reach a max. of 2000 gpm. The potential energy of the source has increased, but only to a limit. [fwiw, at this point the discharge, Fd, is back to 1000 gpm.]

The efficency limits the amount of return flow. It looks like it is simply...

F = Fl/(1 - %eff.)

Is the above correct? Is it not analogous to light flux, too?

As for babble, expressing your ideas succinctly promotes sharper thought!
You may regret this encouragement.

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#### cesiumfrog

If a water wheel is used just to pump water back upstream a little, I think you're right about how much that will increase the flow in that section (although further up or down stream, the average flow rate is unaffected). Offhand, to me, what this really seems analogous to is a dam.

As for light.. sure, you can increase flux inside a resonator cavity (viz. a laser without the gain medium) but the flux that reaches an observer is not increased. (Note, if you really need to change the surface brightness, a gain medium might be what you want.)

Alternatively, say you have a wide beam (stream) of light and (using an arrangement of mirrors) redirect half of the beam onto some second path: Even if both paths overlap later (perhaps halving the total path cross-section so as to double the total flux observed by an instrument there) then the photons in that smaller area will be travelling in twice the range of directions (so that the image sees two images of the beam source, each with the same flux-per-sterradian).

#### Kurdt

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Ahh I see labguy has cleared up my confusion at the original posters idea. Thanks . I knew what he was suggesting was just the same as making a bigger telescope but I was baffled by I know not what.

#### GeorgeSol

cesiumfrog said:
If a water wheel is used just to pump water back upstream a little, I think you're right about how much that will increase the flow in that section (although further up or down stream, the average flow rate is unaffected). Offhand, to me, what this really seems analogous to is a dam.
Ok, but a dam is the heart of the energy source. The discharge is the energy, so the stream is analogous to the light leaving the solar surface. Admittedly, a device which could duplicate the return of energy as in the water wheel example, seems doubtful, to say the least. But, it serves as a stepping stone to show how thermodynamics is not as restrictive as we might think.

Your link to the phase space site, by John Denker, is very good and should finally resolve this for me once I understand it. Of course, it will kill all hope of visual surface brightening. [Not that I didn't know that was where it was heading from the start. I just want to know why and hope for an "if" or a "but" along the way.]

Let me go back to the magnifying glass as it may relate best to the phase space concept. We can burn leaves easily with a magnifying glass by concentrating light from the sun. It combines most of the flux density entering into a small spot because the rays are mostly parallel. Now, move the magnifying glass to the sun's surface and what happens? We will lose this concentration of energy because we lose the advantage of having mainly parallel rays. In fact, the magnifying glass at the sun will not improve the burning time of a leaf compared with not having a magnifying glass (ignoring atmospheric effects which would favor blue photons).

Alternatively, say you have a wide beam (stream) of light and (using an arrangement of mirrors) redirect half of the beam onto some second path: Even if both paths overlap later (perhaps halving the total path cross-section so as to double the total flux observed by an instrument there) then the photons in that smaller area will be travelling in twice the range of directions (so that the image sees two images of the beam source, each with the same flux-per-sterradian).
This makes sense. Yet, the idea of combining light into a scope from an adjacent area seems all to intuitive, though, apparently impossible.

If we consider photons as rubber balls, for instance, we can increase flux density by concentrating a beam of rubber balls with the use of a funnel. And, we can increase the flux density to a concentration that exceeds the original radiating source!

A mirror or lens seems to act just like a funnel, but light seems to defy this analogy. [I am ignoring focus issues at the moment and addressing the claim that we can not increase the energy concentration of sunlight onto any spot greater than the original flux density.]

#### cesiumfrog

GeorgeSol said:
If we consider photons as rubber balls, for instance, we can increase flux density by concentrating a beam of rubber balls with the use of a funnel. And, we can increase the flux density to a concentration that exceeds the original radiating source!

A mirror or lens seems to act just like a funnel, but light seems to defy this analogy. [I am ignoring focus issues at the moment and addressing the claim that we can not increase the energy concentration of sunlight onto any spot greater than the original flux density.]
A better analogy might be billiard balls on a horizontal surface. (Gravitational effects confuse the issue, particularly as surface brightness measurements will be higher from within a gravity well.) Now try to design a funnel shaped bank (the mirror) to concentrate the flux density (assuming the balls originate from all points along some extended line source, perhaps the triangle circumference, and with any possible initial direction).

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