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 Archive 2012 · silly inverse square law question.
curious80
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 p.9 #1 · p.9 #1 · silly inverse square law question.

RustyBug wrote:
Please apply Newton's First Law of Motion relative to your ISL assessment mentioned above.

I am not sure what you are implying but if you are talking about the motion of a single photon then yes it will keep moving in a single direction. Of course we have multiple photons moving in multiple directions here. Lets say we have 100 photons which leave a 1umx1um surfaces of our white paper. Since we have diffused reflection so they are moving in roughly all directions and in keeping with newton's first law they will keep their direction as they move and thus will spread as they go father. Do we have agreement so far?

Dec 11, 2012 at 03:35 AM
curious80
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 p.9 #2 · p.9 #2 · silly inverse square law question.

If it helps here is the illustration from Light, Science and Magic for diffused reflection (I hope it won't be considered copyright violation!):

http://farm9.staticflickr.com/8351/8263396616_dfebf0f0a6_z.jpg

Dec 11, 2012 at 03:41 AM
RustyBug
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 p.9 #3 · p.9 #3 · silly inverse square law question.

Replace the diffuse (variable surface angles) white card in the illustration with a uniform surface and the three cameras will not receive the same reflected light ... because light travels iaw AI=AR.

The camera on the right will receive more light than the other two, based on AI=AR. In a perfect theory (we are talking theory here), the camera on the right will receive all the light (say 100 photons X 1 angle of reflection), while the other two cameras will receive no light.

Now use a reflecting surface that has 3 finite surface angles evenly distributed (33,33,34) to correlate to the even distribution of 100 photons arriving from a single direction, each one of the three angles at the proper angle to reflect the incoming photons directly to each of the cameras. Each camera would then receive 33,33,34 photons, iaw AI=AR.

Now, take that middle camera ... move it back (on axis) twice as far from the reflected surface. What will happen to those 33 photons that were reflected in the direction of the camera?

Will they:

A) Continue to travel in the straight line direction derived from AI=AR, iaw with Newtons' First Law of Motion such that the 33 photons still reach the camera
B) Spread out iaw ISL such that the camera receives only a reduced portion of those 33 photons

Dec 11, 2012 at 04:05 AM
curious80
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 p.9 #4 · p.9 #4 · silly inverse square law question.

Sure. As I have said many times, I don't disagree with AI=AR. What you are describing is why diffuse surfaces reflect light in all directions and I don't disagree with that. What I am talking about is what happens as a result of this reflection in all directions.

Sure most real world surfaces are not ideal diffuse surfaces, but as LS&M says a white card is almost a perfect diffused surface and will make our discussion easier. Once we agree with what happens with a perfect diffused surface like a white (non-shiny) wall or a white card, we can look at other less-ideal cases.

Dec 11, 2012 at 04:21 AM
RustyBug
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 p.9 #5 · p.9 #5 · silly inverse square law question.

curious80 wrote:
Once we agree with what happens with a perfect diffused surface like a white (non-shiny) wall or a white card, we can look at other less-ideal cases

Let me guess, they reflect light iaw AI=AR, predicated upon the variety of surface angles involved ...

The question is why the exposure doesn't change when we move the camera back. My contention is that it is because whatever amount of light is reflected in the direction of the camera, those photons will continue in the direction of the camera iaw with Newton's First Law of Motion, regardless of how far back the camera is moved (on axis).

The reduction in the number of total number of photons being reflected in the direction of the camera is predicated upon the AI=AR, whether that be 1, 3 or the multitude of angles associated with the surface angles involved. The number of surface angles involved will impact the amount of distribution from our originally arriving (single direction) photons. If we had a surface (presumed equal distribution, blah, blah) with 10 angles, then the result would be reflecting 10 photons in 10 different directions, each camera receiving 10 photons, but those 10 photons would still continue along the straight path originating from the AI=AR imparted at reflection ... continuing to the camera regardless of its distance from the subject. AI=AR spreading the 100 photons in 10 different directions of 10 photons each holds Conservation of Energy, just as 100 photons in 3 directions of 33,33,34 holds.

The distribution of those 100 photons by 10 or 3 varying angles, resulting in 10, or 33 photons continuing on the straight line path iaw with AI=AR holds to Newton's First Law of Motion. Thus, neither law is violated.

+1 that most objects fall somewhere between ideal diffuse and ideal uniform surface angles, thus following AI=AR. Which, while an ideal diffuse object may create a wide dispersion of reflected light, reflected light does not travel iaw ISL, it travels iaw AI=AR.

ISL is predicated upon dissemination from a PLS and is omni-directional (i.e. all directions). Reflected light has a finite number of angles involved (predicated upon the array/matrix of incident angles & surface angles to yield the reflected angles produced).

Dec 11, 2012 at 04:46 AM
RustyBug
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 p.9 #6 · p.9 #6 · silly inverse square law question.

curious80 wrote:
Sure. As I have said many times, I don't disagree with AI=AR. What you are describing is why diffuse surfaces reflect light in all directions and I don't disagree with that. What I am talking about is what happens as a result of this reflection in all directions.

SOME of that light is being directed at the camera (angles of inclusion) iaw AI=AR. That light (33 photons, etc.) that is being directed at the camera, continues to travel in the same direction (i.e. toward the camera) as the camera, iaw Newton's First Law of Motion, even if we move the camera back (on axis).

TBC ... manana

Dec 11, 2012 at 05:13 AM
curious80
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 p.9 #7 · p.9 #7 · silly inverse square law question.

RustyBug wrote:
Let me guess, they reflect light iaw AI=AR, predicated upon the variety of surface angles involved ...

I am not sure why we are repeating this again and again when I have said so many times that I don't disagree with AI=AR and how it is the basis for diffused reflection For some reason you have this notion that I do not agree with AR=AI, whereas I do agree with that.

The question is why the exposure doesn't change when we move the camera back.

Exactly so lets discuss that question rather than AR=AI which is already agreed upon

My contention is that it is because whatever amount of light is reflected in the direction of the camera, those photons will continue in the direction of the camera iaw with Newton's First Law of Motion, regardless of how far back the camera is moved (on axis).

The reduction in the number of total number of photons being reflected in the direction of the camera is predicated upon the AI=AR, whether that be 1, 3 or the multitude of angles associated with the surface angles involved. The number of surface angles involved will impact the amount of distribution from our originally arriving

You have suddenly made a jump from sound physics to an assumption which has no scientific reason to support it. We are talking about microscopic surfaces here, with innumerable little micro-facets not 5 or 10 directions aligned with cameras. Lets go back to the LS&M diagram above and consider having a more realistic number of photons i.e. hundreds of thousands of photons. In case of something like a white paper there will be photons moving in all directions, not 10 or 20 fixed directions. And moving the camera back will make some of those photons miss the lens. For a diffused surface and large number of photons the number of photons hitting the lens will drop with distance exactly by the inverse square of distance. There is no scientific reason to support that this will not happen. It is an inevitable consequence of AI=AR.

It is true that real-world objects are not ideal diffused surfaces. Reflected light is typically modeled as a combination of diffused reflected light and direct reflected light (again refer to LS&M and other works on graphics systems). However most non-shiny objects are dominated by diffused reflection and above description predicts their behavior very well. Shiny surfaces with specular reflections need a slightly different treatment to understand their behavior.

ISL is predicated upon dissemination from a PLS and is omni-directional (i.e. all directions). Reflected light has a finite number of angles involved (predicated upon the array/matrix of incident angles & surface angles to yield the reflected angles produced).

Of course actual light sources are not ideal point sources either and they send out a finite number of photons in finite number of directions. However the number of photons and their directions are large enough that we can approximate it as "all directions". This is not a valid basis to try to distinguish them from reflected surfaces which also send light in "all direction" in a similar sense.

Here is another little side question for you to answer. Assume you use a white sheet as a reflector to reflect light on a subject - then would the light falling from the reflector into the subject change when you move the subject away from the reflector? Since you claim that the reflected light will not obey inverse square law so the amount of light falling on the subject should then not change as you move the subject away?. In reality it will drop exactly with square of the distance between the reflector and the subject. Can you please give a reasoning for this drop if the inverse square drop does not apply to reflected light. And can you tell me if there will be any difference in behavior if I replace that white reflector with a light source of the same size? In reality there will be no difference between them in terms of how light falls off with distance. In fact as Helen already pointed out - the light sources such as strobes and flashes typically have reflectors in them and the light that we get from them is mostly reflected light. And I think everyone agrees that these reflected lights obey inverse square law.

Honestly you are fighting a lost cause. There is no sound physics theory which can validate your assumption here. I think this at this point I will again take a leave from the thread as I suspect we are going to get into circles pretty soon again.

Dec 11, 2012 at 06:24 AM
RustyBug
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 p.9 #8 · p.9 #8 · silly inverse square law question.

curious80 wrote:
Shiny surfaces with specular reflections need a slightly different treatment to understand their behavior.

It is a statement like this that renders much disagreement ... maybe even if only pedantic to some, but it is suggestive that the laws of physics of the nature of light do not hold true for all circumstance. It is by definition of a law of physics, that it necessarily does hold true in all circumstance.

The exact same laws of physics determine how light reflects off of a shiny surface, as it does for a diffuse one. This is AI=AR.

Let me offer this ...

ISL is a trigonometric function
AI=AR is a trigonometric function
Light moves with a speed and direction, it is a vector force
Vector forces are a trigonometric function
Light moves iaw trigonometric functions

Light moves iaw trigonometric (vector force) functions. ISL is a specific explanation of a specific omnidirectional non-reflected scenario (iaw trig) AI=AR is how reflected light changes direction when acted upon by an outside force (iaw trig), i.e. the object it is reflecting off of. Reflected photons continue to follow the straight line path of their AI=AR iaw with Newton's First Law of Motion.

You seem to be intent on wanting to take it from diffuse and work backwards, making allowances to explain for special cases. I seem to be intent on taking it from singular photon, the nature of light, and work it forward holding fast to the tenets of the law @ AI=AR for all things.

As I mentioned to Helen & you earlier, I think that we'd eventually find the "missing link" that is garnering the distinction from which we are misunderstanding each other. I will hold fast to AI=AR, (opaque, translucent, transparent, index of refraction, etc.) for reflection/refraction (i.e. outside force acting upon), Conservation of Energy and Newton's First Law of Motion in regard to reflected light.

As to your question @ using reflectors, also consider the parabolic reflector/umbrella, or the beauty dish. These are all simply variations of intentionally designed applications of AI=AR. Whether, you are diffusing or concentrating or collimating light ... it is always a product of AI=AR. There are no "slightly different treatments" required, only a full cognizance of all the factors involved for a given scenario.

Again, consider the parabolic reflector ... which depending on the distances involved (before or after "crossover"), may either have the "effect" of concentrating or diffusing, but it still is a byproduct of AI=AR.

I offered impasse earlier ... I'll offer again.

Edited on Dec 11, 2012 at 12:02 PM · View previous versions

Dec 11, 2012 at 11:24 AM
HelenB
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 p.9 #9 · p.9 #9 · silly inverse square law question.

Rusty, I think that you are ignoring the fact that the lens' entrance pupil has a finite diameter.

On a different point, if you are considering a perfectly reflecting surface then the light behaves as if it is coming from the reflection of the source(s), not from the surface itself. The inverse square law applies to the distance along the light path from the source to the camera, not the surface to the camera. A diffusely reflecting surface acts as if it were a light source itself, in terms of the distance/area flux relationship.

Dec 11, 2012 at 11:30 AM
RustyBug
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 p.9 #10 · p.9 #10 · silly inverse square law question.

No, I haven't ignored it ... we just haven't gotten there yet.

Until we properly apply how light moves, it's premature to discuss how it is viewed, or how it "acts like" some other case. The explanation of why it "acts like" is rooted in the full entity of factors involved relative to vector forces (which btw, are responsible for securing Conservation of Energy) and Newton's First Law of Motion.

Pardon me, if I sit down for a bit ... weariness is waning my enthusiasm, and I'm not sure that I want to continue to a full blown course in optics ... beyond the fundamentals of how light moves, iaw AI=AR. Without agreement that it holds true in all applications, I really don't see how we could ever find the "missing link" that is keeping the camps divided and the subsequent explanation of things observed that are trying to be explained by "acts like" and "slightly different treatment".

My wife is about to kill me already for the amount of time, energy & effort I've put to this to date ... I hope you (and fellow FM'ers, participating or lurking) understand. I need to hang Christmas lights and a whole slew of other things.

Dec 11, 2012 at 11:48 AM

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Guari
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 p.9 #11 · p.9 #11 · silly inverse square law question.

RustyBug wrote:
My wife is about to kill me already for the amount of time, energy & effort I've put to this to date ... I hope you (and fellow FM'ers, participating or lurking) understand. I need to hang Christmas lights and a whole slew of other things.

Same here... Have a nice christmas guys and gals..

Dec 11, 2012 at 12:01 PM
RDKirk
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 p.9 #12 · p.9 #12 · silly inverse square law question.

Rusty, I think that you are ignoring the fact that the lens' entrance pupil has a finite diameter.

That is the point. That is why the lens captures only coherent rays and does not capture diverging rays.

The lens only captures the light that is headed directly toward it.

Dec 11, 2012 at 12:19 PM
HelenB
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 p.9 #13 · p.9 #13 · silly inverse square law question.

RDKirk wrote:
HelenB:"" end HelenB quote.

That is the point. That is why the lens captures only coherent rays and does not capture diverging rays.

The lens only captures the light that is headed directly toward it.

That makes no sense logically, and it is also completely wrong.

The fact that the entrance pupil has a finite diameter allows it to capture divergent rays, and that is exactly what it does.

Dec 11, 2012 at 12:45 PM
HelenB
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 p.9 #14 · p.9 #14 · silly inverse square law question.

Rusty, your last statement suggests to me that the reason you are having this problem is that you are ignoring the size (angular diameter) of the entrance pupil. I have tried to raise this before. It is critically important. Nobody is arguing against the idea that a photon travels in a straight line with constant energy.

Dec 11, 2012 at 12:51 PM
RustyBug
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 p.9 #15 · p.9 #15 · silly inverse square law question.

I'm really not having any trouble with most any of this ... other than the statement that reflected light travels iaw ISL, and things like "slightly different treatment" being needed to explain different scenarios, etc.

I totally get the angles involved, including those that are coherent, divergent and convergent relative to the angles of inclusion being seen through the entrance pupil at angles that will be captured within the area of the film plane ... stemming from the direction the light is traveling once it leaves the object it is reflecting off of.

I'm good with it all ... it's just my ability to explain that is seemingly "not so good".

Dec 11, 2012 at 01:07 PM
RustyBug
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 p.9 #16 · p.9 #16 · silly inverse square law question.

HelenB wrote:
The fact that the entrance pupil has a finite diameter allows it to capture divergent rays

+1 @ within the confines of the angles of inclusion, it can capture some divergent rays.

Hold on ... now, here's where the "Big Rub" comes with most all of this ...

ISL ... always produces divergent paths of light.
AI=AR can produce divergent, convergent or coherent paths of light.

The statement that reflected light travels iaw with ISL thus implies that reflected light is always divergent ... this is the part that I have my most ardent objection to.

Allowing light to continue its reflected path (predicated on AI=AR) iaw Newton's First Law of Motion ... yields that some of the light is traveling in divergent, convergent and coherent light paths (i.e. the array that I spoke of way back). The rest follows suit as the light that reaches the entrance pupil (angles of inclusion) and passes on to the film plane, accordingly.

Changing the camera position will have no effect on those rays that are traveling coherently, It will have some effect (angles of inclusion) on those traveling divergently and convergently. It isn't an ISL offset that retains the exposure irrespective of camera - subject distance ... it is the tradeoff of reduction of divergent paths, simultaneous with an increase in convergent paths (or vice versa) that occurs when camera-sujbect distance is varied (on axis). I tried to illustrate this (failing miserably) with my inept drawings earlier.

I think it bears repeating ... again:

ISL always produces divergent light paths.
AI=AR can produce divergent, convergent or coherent light paths.

Edited on Dec 11, 2012 at 01:44 PM · View previous versions

Dec 11, 2012 at 01:13 PM
HelenB
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 p.9 #17 · p.9 #17 · silly inverse square law question.

You have it upside-down. The inverse square law is a consequence of the conservation of energy. It isn't a law that controls reflection at a surface. It is about what happens next.

Are you happy about light from a diffuse reflector being divergent from the reflector surface? Are you happy with the quote from LS&M with respect to secular reflection?

Dec 11, 2012 at 01:43 PM
HelenB
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 p.9 #18 · p.9 #18 · silly inverse square law question.

Have any of you doubters read the classical treatment of this subject, in either Born and Wolf or Ray? Would it help if I spent the time to go through it with you? Why didn't the quote from LS&M clinch it?

Dec 11, 2012 at 01:48 PM
RustyBug
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 p.9 #19 · p.9 #19 · silly inverse square law question.

LS&M quote cited example ... they moved the mirror closer to the diverging (ISL) light source, not the camera farther from the mirror reflected iaw AI=AR (in that illustration). See other sections @ angles of inclusion where they do move the camera farther from the reflected source, iaw AI=AR that can be either divergent, convergent or coherent.

HelenB wrote:
The inverse square law is a consequence of the conservation of energy.

ISL diffusion is the natural order of matter dispersing from greatest concentration to lesser concentration without an outside force acting upon it.

It is not a consequence of the conservation of energy, even though it adheres to conservation of energy by virtue of its trigonometric vector forces involved that when summed will yield consistent.

We are in "Cart & Horse" territory here.

Probably best to impasse.

Feel free to continue with Ray and company as you see appropriate. I feel that with the realization at ISL always divergent vs. AI=AR yielding divergent, convergent and coherent paths ... those who have been trying to discern the great divide between the camps, this (imo) is sufficient (for the audience of FM'ers) to see why we disagree so ardently ... and conducted in good spirit of good FM'ers I might add.

I'll rest and stand on AI=AR vs. ISL ... both being trigonometric functions pertinent to vector quantities, with ISL always producing divergent paths, whereas AI=AR may produce divergent, convergent or coherent paths ... and the rest follows as noted above per Newton's First Law of Motion.

Dec 11, 2012 at 02:01 PM
HelenB
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 p.9 #20 · p.9 #20 · silly inverse square law question.

If you wish to leave it as an impasse then fair enough. Could you, for the sake of people reading this to try to make their own mind up, describe your answer to the original question in a concise and clear manner? If there is no IST falloff in energy flux through the entrance pupil as distance changes, how come the image brightness does not change as the image size changes? Why, if in the case in which the entrance pupil diameter and distance to the subject is fixed (and hence energy flux is fixed - I assume we agree on that), does image magnification then affect image brightness?

Dec 11, 2012 at 02:33 PM
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