RustyBug
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 p.10 #8 · silly inverse square law question. | |
The "some" was accounting for light originating from multiple directions (i.e. diffuse lighting) reflecting off a diffuse surface, where "some" of the angles stemming from AI=AR would previously not have fallen inside the family of angles, now do. This was not to suggest that the light was not traveling in a straight line, on axis (significantly).
If you recall ... I (along with others) had argued against the entire ISL notion from the beginning, begin predicated upon the "straight line" travel, iaw AI=AR ... only to be told that we were wrong. If you also look back, you'll see where I referenced the bisection of an angle having no bearing from the length of the ray.
As I mentioned quite some time ago (on a couple occasions), the problem that people are having with this is that they are not fully accounting for the matrix array of incident light angles combined with the variants of surface angles (based on their observations and presented scenarios).
It is this vast array that makes people tend to think that ISL (or some form of divergence thereof) is in play. It is only the complex array of AI=AR that is happening ... and continuing on straight line paths, iaw Newton's First Law of Motion.
If you'd like to take a stab at walking us through a single photon originating from its source, reflecting off an object, passing through the entrance pupil and reaching the film plane, I would be interested to see how you present the travel of that light/energy.
Every aspect of how this plays out is predicated upon how a single photon moves. The rest is simply the mass collection of the array. It is the magnitude of the array that is keeping people from getting their head around it as they try to use what they "observe" .. in conjunction with some aspects of something (ISL, etc.) that they've been told about ... rather than a fully accounting for / understanding what is actually happening. But first, we need to start with a single photon:
Here is my stab at a "portrayal" for how a single photon goes from its source to our camera (sans the lens optics) ...
1. Photon leaves source in a given direction, containing a given amount of energy
2. Photon continues that path in a straight line, iaw Newton's First Law of Motion until acted upon by an outside force.
3. Photon has some value of energy absorbed, reflected or refracted by the object it interacts with, iaw with the properties of that object (opaque, translucent, transparent, color).
4. The remaining energy that is neither absorbed (color) or refracted (index of refraction) is reflected iaw AI=AR relative to the angle of incidence with the surface at the point it was acted upon by the object. (Energy is conserved @ absorption + refraction + reflection)
5. The photon continues in a straight line path, iaw Newtons's First Law of Motion.
6A. IF the direction of that photon is contained within the family of angles that is "seen" by the entrance pupil, then that photon will pass through the entrance pupil and proceed to strike either the sensor or film at the film plane where the energy it left the object with, is then converted into an electrical signal or chemical change to the film (and some heat).
6B. If the direction of that photon is not contained withing the family of angles that is "seen" by the entrance pupil, then that photon will not pass through the entrance pupil and will not reach the sensor or film at the film plane.
AI=AR, Newton's First Law of Motion, Conservation of Energy ... whether for a single photon (one bouncing ball) or a google of photons (a whole bunch of bouncing balls).
That's my story and I'm sticking to it. 
While we don't have a practical source that generates a single photon in a single direction (billiard table provides practical emulation), understanding how one moves is paramount to understanding how more than one moves. When a point light source generates a volume of photons, those photons are dispersed in an omni-directional spherical distribution pattern, iaw ISL. Every photon leaving its PLS source has a direction in which it is traveling. The number of directions is beyond a practical ability to individually draw/illustrate, so we simply reduce such conceptual illustrations/drawings to an over-simplified representation.
The book Light: Science & Magic has a chapter (CH. 3 in the third edition) on the management of reflection and the family of angles. It is the family of angles, that LS&M does a nice (simple & practical) job of illustrating the concept that both on-axis and off-axis, non-parallel light rays can enter the camera. LS&M carries the family of angles forward throughout the remainder of the book. In Chapter 6 (3rd edition), figure 6.18 shows how the family of angles change when the camera position is moved farther from the subject (the original question, lest we've forgotten).
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=AR) when it is farther that are reflecting off the object.
I realize that this is initially going to cause some angst for some people trying to get their head around it, but it plays out just fine, if we will follow things forward appropriately. It also gets a bit "convoluted" for some, because the illustration introduces a different lens to retain similar image magnification. This would prompt some to argue that it can't be receiving fewer photons when it is farther away, or else the exposure wouldn't be the same. At face value, that makes common sense. However, the physical size of the aperture for a longer lens @ f8 is larger than the physical size of the aperture for a shorter lens at f8. The f stop value is a proportional value that compensates for the variance in FL, it is not an absolute value. Thus, it has a 'built in" compensation, if you will. You can do the math for the different physical size apertures and see that there is an offsetting change in the family of angles for the number of photons, but I'll pass atm.
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
Based on the above, I continue to adhere that it is not some post-reflection, "offsetting ISL" explanation (remembering Newton's First Law of Motion). It is 100% AI=AR, fully developed to account for all the changes in the trigonometry of vector forces involved ... i.e. follow the bouncing balls. 
Also, please note that while some will want to re-introduce the diffuse surface "acts like" ISL concept, because some of the light is being reflected into different directions "not seen" by the camera, we should realize that that light has already been removed from the exposure equation by virtue of AI=AR has placed those photons outside of the family of angles, thus it is rather moot to try and apply ISL theory to what is truly a matter of AI=AR.
As you can "see" there is a tremendous amount of light that gets "wasted" as light is emitted from a PLS iaw the spherical distribution pattern of ISL, that does not fall within the family of angles, unless we intentionally use AI=AR to "reshape" the distribution pattern. This is what all light modifiers seek to do.
Feel free to present your "portrayal" of a single photon for contrast / comparison. But more importantly, please read and study the entirety of LS&M to for its practical utilization, and see how it is rooted in AI=AR.
HTH
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