silly inverse square law question.
/forum/topic/1162172/9

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 RustyBugRegistered: Feb 02, 2009Total Posts: 13590Country: United States Glad you understand. As to the reasoning why ... without going through all the iterations, I tried to explain the offset associated with distance change in a previous post (excerpt below). As mentioned earlier at the language of flux energy, etc. I'm a bit remiss. I must simply hold true to the most fundamental of principals and apply them without violation to foster my understanding. This is likely the best I can do atm ... sorry if it is perceived as incomplete, but I simply follow the bouncing ball(s). Those that bounce in, get in ... those that bounce out, don't. From post pg. 9, #16: 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.

 HelenBRegistered: Dec 10, 2012Total Posts: 59Country: United States Interesting. Have you ever found that explained, or even mentioned, in any textbooks or anywhere else on the web? It differs quite a lot from the classical explanation, which is what curious stated on page 1. How does the convergent-divergent mix of light fit in with having the surface in focus? You are saying that there is some ISL effect (the loss of divergent paths as you get further away), but that is made up for by an increase in convergent paths. That convergent part gives me a big problem. Where do these convergent paths originate? Where do they end up? (I assume that we are talking about a focused image) How can you ignore energy conservation? I think that you have to address that because it is energy that determines image brightness. Accounting for the different image areas is not optional in this discussion - it is an integral part of it.

 RustyBugRegistered: Feb 02, 2009Total Posts: 13590Country: United States See feeble, inept illustration @ page 4, #17 Note loss of red/yellow, add of blue. Grossly oversimplified, but the concept of some previously out, now in ... some previously in, now out ... illustrated. Throw a football through a tire ... stand really close to it, you can throw the ball through it from a given set of possible angles. Move the tire back, and the number of angles in the set of possibilities at which the football can pass through the tire (from the new distance) is different. Correspondingly, the range of places in which the footballs can land, after passing through the tire is different for the variant distances between thrower and tire. Of course, we could move inside to the billiard table too. Meet me at the pub and this will be done & over in about 2 minutes using a 9 ball rack for the aperture and a couple 8 ball racks for the film plane. After that, the beer's on me.

 curious80Registered: Jun 18, 2010Total Posts: 1455Country: United States RustyBug wrote: ... I think it bears repeating ... again: ISL always produces divergent light paths. AI=AR can produce divergent, convergent or coherent light paths. I feel that we have aligned our frames of reference enough that it might be possible to get a consensus after all, so here I am again I agree to a lot of what you say: 1. I fully agree that AI=AR is the governing principal for reflected light 2. I also agree that AI=AR can produce all types of light paths including divergent, coherent etc The only part that I disagree with is your notion that when you move the camera back, the amount of light entering the lens dos not change. To support that you present the notion that somehow all the lights rays that get reflected from the subject towards the camera are coherent - that assumption is unsupported and not true in general. The reason I have stressed the diffused case is because it is very easy to see that your assumption does not hold in that case. If your assumption is sound then it should surely hold in all cases including the everyday case of a white paper or white wall, or in fact most other objects because most objects that we photograph are primarily diffused surfaces. I think the difference is coming from what the terminology as well. When I say ISL I just mean the general behavior where light intensity falls with the square of the distance, I don't care about which specific physical phenomenon caused this falloff with distance. You on the other hand seem to tie the term ISL with a specific physical phenomenon. To get over obstacle that let me drop the term ISL all together. So basically what I am saying is that due to the implications of AI=AR the reflected light intensity also falls inversely with square of the distance. As has been pointed out this holds for a variety of diffused and non-diffused cases: the case of photographing a white surface (diffused), the case of using a white sheet as a reflector to fill light on a subject (diffused), the case of reflector in the umbrella (mostly direct reflection and not as much diffused) and the case of a mirror (completely direct reflection). Basically it holds for all the cases which we typically find in the world around us and that we will find when doing photography. I also agree with you that this behavior is not fundamental to reflection. For example if we shine a laser on a mirror, the reflected light will also be a coherent beam.

 curious80Registered: Jun 18, 2010Total Posts: 1455Country: United States RustyBug wrote: 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. I just mean that the microscopic details of how the light rays bounce around would be different because the surface structure is different. The governing laws are of course the same. 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. Agreed. (Well actually there is a bit more to it than AR=AI. All surfaces other than perfect ideal mirror surfaces absorb part of the light. That light undergoes random scattering under the surface and then some of that light escapes out again at random angles. But we can ignore that for this discussion and focus on AR=AI). Light moves iaw trigonometric (vector force) functions. ISL is a specific explanation of a specific omnidirectional non-reflected scenario (iaw trig) It would not matter whether it is reflected or non-reflected. Surely you would agree that in those cases where AI=AR results in divergent omni-directional beams, the intensity would still fall off with square of distance. You are right though that ISL only applies when the light flow is omni-directional. So if reflected light is for example completely coherent then there would be no drop in intensity with distance, just like ISL does not apply to coherent light sources like lasers. (Well the light flow doesn't have to be omni directional. Even if the light flows out uniformly in a cone, ISL still applies. Real light sources like soft boxes etc are not really omni directional, but send out light in a cone, but I think we both know what we mean here) 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. Agreed. 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. No. I just take diffused case as an easy to discuss example. All cases including the diffused and non-diffused cases can be explained by detailed study of AI=AR as well as the motion of rays after the reflection. 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. So do I, as I have mentioned on a number of occasions now I just think that you are refusing to accept some implication of AR=AI. I have shown those implications for the specific example of diffused surfaces, again because that is easier to analyze. I have explained how AR=AI predicts an inverse square drop off at least for that particular case, and you have not addressed that so far. 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 I agree. The behavior is determined by the AR=AI in all cases - to that end we have no disagreement. What I am pointing out is that in both the case of a white sheet reflector (diffused) or a say a silver reflector (not diffused) we will have the reflected light dropping off with inverse of the distance. I hope you don't disagree that this is true at least for these specific cases (under the AR=AI no doubt ). And yet when we photograph these, they will have constant exposure when we move the camera away, even though the light intensity is falling with distance. So I am interested in knowing why in your opinion the exposure does not change if you photograph say a white reflector from increasing distances, when we know that the light reflected from that reflector drops with intensity. And yes I agree that there will be other scenarios where the reflected light intensity will not fall with square of the distance, depending on the specific AR=AI arrangement. However those cases are not going to follow the constant exposure either.

 ross attixRegistered: Jan 29, 2005Total Posts: 67Country: United States Ok. I see I'm late to this discussion, but good for you for starting it. I won't repeat what many others have said, but in a related situation I always wondered why people bracket for exposures of the moon. It is the sunny 16 rule.

 HelenBRegistered: Dec 10, 2012Total Posts: 59Country: United States Apart from the problems I have already mentioned, there is another big problem with the 'some rays that were in are now out, some rays that were out are now in' theory. If an on-axis or near-axis area element of the object is imaged when the camera is close, the rays that form that image include all the rays that could possibly form the image of that same area element when the camera is moved away (assuming constant aperture, and lens axis). It is impossible, because light travels in straight lines, for any extra light from that area element to reach the camera (strictly speaking the entrance pupil) as it is moved away.

 RustyBugRegistered: Feb 02, 2009Total Posts: 13590Country: United States curious80 wrote: we know that the light reflected from that reflector drops with intensity. This is not true (physics). A single reflected photon carries its reflected energy (conservation of energy) in a straight line until it is acted upon by another outside force. What is true is that a reflector changes the direction of the multiple photons that are striking it (and subsequent distribution pattern thereby created). If those photons are being divergently reflected, their concentration will diminish for a given area at increasing distance, iaw the trigonometric functions of the angles at which they are traveling. Conversely if those photons are being convergently reflected, their concentration will increase for a given area at a given distance, until they reach the "cross-over" point at which they will then be on divergent paths. This can be seen with things like magnifying glass, parabolic mirrors, etc. which also is responsible for why an image changes from inverted to normal on either side of the convergent / divergent crossover point. Thirdly, if those photons are collimated into parallel distribution paths, their concentration for a given area will remain constant at any distance. The directions of the multitudes of photons will reflect iaw, AI=AR, with real world application being that a variable number of AI's (family of angles) strike a variable number of surface angles to generate a variable number of AR's. Only those that are within the realm of the "family of angles" will reach our camera. Please note ... there is difference between the practical observation of that which we have come to accept and frequently apply vs.the actual physics taking place. They question @ why something happens has to be answered by the physics, not simply a practical observation. Granted ... discovery begins from practical observation, but the law of physics hold true even when we may not realize that degree to which we are not seeing them occur.

 HelenBRegistered: Dec 10, 2012Total Posts: 59Country: United States RustyBug wrote: Noting particularly that the family of angles that can be "seen" by the entrance pupil does in fact change. Notice how that with the family of angles being different, the number of directions from which light is originating, is varied. The more distant camera position corresponds to a more narrow family of angles from which to receive the light via reflection. The closer camera position corresponds to a wider family of angles from which to receive the light via reflection. By virtue of the fact that the different camera position can see "more" or "less" of the light being dispersed from its source, it now receives more photons (iaw AI=AR) when it is closer, and fewer photons (iaw AI= Lets, move back to the point at the original question about simply moving the camera farther back (i.e. no lens change). If we follow the light from the source, and accept that moving the camera farther back from the reflecting object changes the angles from which can be "seen" by the entrance pupil, we can also see that it will allow fewer photons to pass through the aperture. Fewer photons would mean "less light" ... which makes bells and whistle start going off at exposure change. But, in concert with that "less light" / fewer photons passing through the entrance pupil/aperture, the projected image is also smaller. As such, we have a corresponding reduction in image size, along with a corresponding reduction in photons (originating from the source as restricted by the family of angles). Move in closer, more photons, larger image ... thus the density of photons being spread over the given area remains constant, irregardless of the distance, due to the simultaneous change in image size and number of photons being received, iaw with AI=AR as constrained by the accompanying change in family of angles. THIS IS WHY the exposure hasn't changed. Fewer photons spread out over a smaller area vs. more photons spread out over a larger area. The "butter" that LS&M uses for an analogy holds true, and the exposure doesn't change That is exactly what I have already stated. I have no idea why you have disagreed with it. The number of photons passing through the entrance pupil reduces in inverse proportion to the square of the distance, while the area they cover also reduces in the same manner. There are no 'extra' photons arriving to balance the loss of others as you have claimed (for on-axis corresponding object and image area elements). Off-axis area elements may, of course, behave differently (ie the brightness of their image may change), principally because of directionality effects and cos^3 or cos^4 effects as the angle from the local object surface normal to the center of the entrance pupil changes. No general rule can be made about that because it is influenced by the surface's particular reflection indicatrix (reflectance pattern with respect to angle of incidence), the angle of illumination of that object surface (and for images of sources themselves the directional properties of that source) and whether or not the particular lens has a tilting pupil.

 RustyBugRegistered: Feb 02, 2009Total Posts: 13590Country: United States The point of distinction in the difference is the inclusion of more (or less) light from the source being available to meet the constraints of the AI=AR to reach the entrance pupil with the varying distance based on the varying family of angles that accompany such changes. It is not because the light "falls off, iaw ISL" post reflection. It is because the angles have changed from which the object to receive/reflect the light ... adhering to the tenets of the trigonometry for vector forces involved. I think that while we are much more in agreement now regarding the energy flux that you have referenced, my distinction is that the delta is predicated upon the change in the light falling upon the reflecting object (by the change in family of angles), rather than a dispersion post-reflection. The issue of "family of angles" is the critical aspect involved here. LS&M devotes a chapter to it, and then continues to use it throughout the remainder of the book ... striving to focus on the light that you are working with, moreover than the light you aren't, and showing how to distinguish between the two.

 HelenBRegistered: Dec 10, 2012Total Posts: 59Country: United States It's the same thing. You are making a distinction where none exists. You are treating the ISL as if it is itself a fundamental law that governs the behavior of light when it is no more than a consequence of the conservation of energy, which does govern the propagation of light. As you have demonstrated, it is followed in this case, ie the observed phenomenon and explanation does not contradict it. Assuming that it is true is not necessary as a first step (nor is it the first step in the reasoning I gave): the assumption of conservation of energy gives a result that does not contradict it. At least we are all agreed that the reason that the image of an object does not get dimmer as you move away from it is that the reduction in energy flux through the entrance pupil (that energy flux being in inverse proportion to the square of the distance, by conservation of energy), is exactly matched by the reduction in image area.

 AccessRegistered: Jun 07, 2004Total Posts: 1577Country: United States I vaguely remember this kind of thing from my physics teacher who explained that inverse square was from a perfect point source and that a perfect linear source would be 1/r and a perfect planar source would be 1. And that most light sources we have today (in reality) are somewhere in between these three, for instance an incadescent bulb or the sun might be close to a point source (though the sun being so far away, our inability to change our relative distance toward/away from it), a flourescent lamp, somewhere between a point source and a linear source (depending on it's relative length and dispersion), and once you start playing with reflections and lenses then you can create things that are closer to planar sources; like the beam of a perfect flashlight that spreads out only slightly over a long distance. In photography you have another issue of importance, relatively light source size. An object like a softbox or umbrella, creating a large light source that is diffuse enough, it will illuminate a given point on the subject from multiple directions, which is desireable. http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html click on 'light on vision' Overall it's a very useful resource, though a bit dated. 10 pages of 'discussion' that one does not have time to read, really people ought to learn the skill of applying knowledge and then just take it from there. There is no need to debate, or even explain one's knowledge, neither of these things changes reality. Our only real use of knowledge is to _apply_ it to what we do, in this case, photography.

 RustyBugRegistered: Feb 02, 2009Total Posts: 13590Country: United States HelenB wrote: You are treating the ISL as if it is itself a fundamental law that governs the behavior of light. Actually, no I'm saying that it is NOT a fundamental law that "governs" the behavior of light. I'm saying that it is a fundamental law that "follows" the behavior of light (matter/energy) being distributed when no outside force is acting upon it and is spherically distributed iaw the trigonometric functions from a PLS. One is ascribing ISL to the cause, the other recognizing it as a symptom. I'll readily agree that most of the practical application of photography is taking light originating from a diverging multitude of angles ... but reflection follows AI=AR, and the light continues to travel in a straight line path in that direction, retaining the energy contained therein. Pedantic to most I'm sure. But, whether one ascribes to my explanation or not ... move the camera back, the exposure doesn't change. That much, we all agree on. That, and it's time to go shoot, rather than talk. It's been a good dialogue, and I think we're about as close as we'll get as I think this one has boiled down to some "lead/lag" perspective at "cause vs. symptom". Hopefully, I've shown it all the way through, from origination, through reflection, to capture ... at least I've certainly given a much stronger effort to do so than I ever envisioned, when I first espoused, it is AI=AR. Again, Welcome to FM ... you have certainly shown yourself to be, imo, a valued member. If you, Curious80, et al are ever my way ... first one's on me. Time to go get one.

 HelenBRegistered: Dec 10, 2012Total Posts: 59Country: United States In that case I have no idea why you disagreed with anything I said. I am glad that the concept of extra photons arriving (your blue rays) has been dropped. They are coming from a different part of the object and will arrive at a different part of the image.

 RustyBugRegistered: Feb 02, 2009Total Posts: 13590Country: United States Well, I said early on I wasn't following your "energy flux" and there was a "missing link" for me. The only way I knew to go, was to walk it all the way through, holding true to AI=AR. It was the whole ISL and "acts like" ISL being the post-reflection cause (not yours) that threw everything into a tizzy that got so convoluted trying to unravel ... thus, I simply started at the beginning and worked my way through it. Yes, I know that my "blue rays" drawing was inept (previously acknowledged) at trying to diagram the family of angles and the corresponding variance in incident light, thus the straight line reflected energy flux via AI=AR. The diagrams in LS&M do a far better job ... thus my repeated recommendation for it to others. BTW .. thanks for your contribution, understanding, patience and assistance ... good FM'er that you have clearly shown yourself to be.

 YonkersRegistered: Feb 06, 2004Total Posts: 159Country: United States Totally fascinating discussion. I read every post and that's saying something in a thread 10 pages long. I understood most but not all of the science but great nonetheless. BTW, curious and HelenB's explanations make sense to me but what the heck do I know. I'm subscribing to see if we'll get a consensus before the apocalypse.

 Doug QuanceRegistered: Mar 07, 2004Total Posts: 3038Country: United States Fascinating discussion. Thanks to all who participated.

 cgardnerRegistered: Nov 18, 2002Total Posts: 9376Country: United States Now that's settled can we move to something else that has always bothered me? How many fairies CAN actually dance on the round head of a pin? If they all fly off the pin with an even distribution outward outdoors how will I know how many will smack the front element of my camera lens like bugs on a windshield? I need to know how much lens cleaner to buy. What happens indoors? Will the fairies bouncing off the walls and ceiling also hit the lens? If so it would seem I'd need more lens cleaner when shooting inside vs. outdoors. Is this assumption correct? What if the head of pin is flat, not round? Will that affect how many dead fairies I'll need to clean off the front element?

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