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 Archive 2012 · silly inverse square law question.
RustyBug
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 p.7 #1 · p.7 #1 · silly inverse square law question.

Curious80's indication that light travels iaw ISL after interacting with another object / outside force is in direct violation of Newton's First Law of Motion.

Since his entire explanation is rooted in this faulty premise ... his explanation is faulty. It seems plausible only to those who ascribe to the notion that Newton's First Law of Motion doesn't hold true (or don't recognize the violation contained therein).

Dec 10, 2012 at 02:57 PM
HelenB
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 p.7 #2 · p.7 #2 · silly inverse square law question.

It isn't a faulty premise.

Light does travel in accordance with the inverse square law after it has reflected off an object (as long as it is not collimated: in most cases it isn't). The inverse square law is nothing other than a statement of the conservation of energy, and it does not contradict any of Newton's Laws of Motion. (Thank goodness). If it did not travel in accordance with the inverse square law, we would either be in deep trouble, or have found free, limitless energy.

The object luminance {cd/m^2, or lx/(steradian.m^2) or radiance in W/(steradian/m^2)} – ie the energy flux (lx or W, ie power) from a given area element of an emitting or reflecting surface in a given direction over a given solid angle – is constant. That is a consequence of the conservation of energy. (1)

As a lens of fixed entrance pupil area moves further from the object, the solid angle the fixed entrance pupil subtends at the object decreases according to 1/r^2, thus the energy flux through it decreases according to 1/r^2. (2)

Dec 10, 2012 at 05:56 PM
RustyBug
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 p.7 #3 · p.7 #3 · silly inverse square law question.

Are you saying that a single photon reflecting off another object will "spread out" and weaken as it travels?

Edited on Dec 10, 2012 at 06:42 PM · View previous versions

Dec 10, 2012 at 06:07 PM
HelenB
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 p.7 #4 · p.7 #4 · silly inverse square law question.

No, but images are made from multiple photons. The closer you are, the more you will catch, keeping the entrance pupil area constant.

Is there anything specific you object to in my previous post?

Dec 10, 2012 at 06:23 PM
RustyBug
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 p.7 #5 · p.7 #5 · silly inverse square law question.

HelenB wrote:
No, but images are made from multiple photons.

Which makes it an array of changing angles iaw AI=AR (as previously stated).

Those that are reflected on a path that is directed to the camera will continue to reach the camera with the same amount of energy whether the distance is 10 feet or 100 feet ... without any loss of energy.

Those photons that have been redirected (iaw AI=AR) will continue toward the camera whether it is one inch or one mile away. Its no different (sans gravity's vector force and air friction) than throwing a baseball in space ... that baseball will continue to travel in THAT direction at THAT speed (definition of velocity) forever until acted upon by another object. When it does interact with another object, some of that energy will be absorbed by the object it hits. It will then reflect off that object and now be traveling in a different direction at a different speed (color wavelength) and will continue to travel in THAT direction at THAT speed forever until it is again acted upon by another object.

Now, If I throw twenty baseballs (yeah, I got big hands), they will go off in different directions. But, for those that hit an object, they will all bounce iaw with AI=AR. Granted they started their travel in a multitude of directions, thus they will bounce off the object at varying directions based on the AI. Now, if just three of those balls happen to bounce straight toward your camera at twenty feet away, moving your camera to either 10 feet closer or 100 feet farther (on axis) ... the camera will still be in the path of those baseballs (i.e. photons). The speed, direction and mass of them is the same @ 10, 20 or 100 feet. They carry the same amount of energy and it will hurt just as much to get hit with a 100 mile/hr fastball at 10 feet as it does a million miles away (in space).

Dec 10, 2012 at 06:43 PM
RustyBug
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 p.7 #6 · p.7 #6 · silly inverse square law question.

HelenB wrote

Is there anything specific you object to in my previous post?

Just that I'm a bit rusty in that particular area computation to either agree or disagree at what you've presented. I'd have to come up to speed and chew on it to either confirm or refute. My initial thought is that you seem to be well presented, so I'll accept it at face value for the moment ... although, I'm not sure as to its applicability or inapplicability atm.

Edited on Dec 10, 2012 at 06:58 PM · View previous versions

Dec 10, 2012 at 06:56 PM
RDKirk
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 p.7 #7 · p.7 #7 · silly inverse square law question.

The inverse square law applies to a point source. In fact, few objects are true point sources.

But relative to practically everything we see, our camera lenses and eyeballs are "point receptors." In other words, we don't see or photograph anything by diverging rays, but only by converging (at very short distances) or parallel rays (at any distance). All those objects emit or reflect light in a multitude of directions, but they all emit bundles of very-close-to-coherent parallel rays.

If we see it at all, it's because those rays by which we see it are parallel or (at very short distances converging). But mostly parallel.

The diverging rays exist, but simply aren't captured. The parallel rays we see obey the laws that RustyBug discusses.

Dec 10, 2012 at 06:57 PM
Guari
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 p.7 #8 · p.7 #8 · silly inverse square law question.

reflecting surfaces do not act as point sources. This has been repeated ad nauseum in this thread.

Dec 10, 2012 at 07:04 PM
HelenB
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 p.7 #9 · p.7 #9 · silly inverse square law question.

There is a huge flaw in that argument, and it is a huge red herring. Sure, the individual photons will not lose energy, but the number of them that will pass through the entrance pupil will change as the distance to the entrance pupil changes (and hence the solid angle subtended at the object by the entrance pupil).

If only three baseballs hit the entrance pupil at 10 feet away, and the same three baseballs hit the entrance pupil a million miles away, what happened to all the baseballs that could have hit the entrance pupil 10 feet away, but missed it at a million miles away? Were there any? If there weren't then the object point would not be visible if you moved the camera just one entrance pupil diameter tangentially from where it is when it 'sees' the object point (at the million mile radius). If there were other baseballs then some of those baseballs would have hit the entrance pupil when it was closer.

Your theory would also predict that entrance pupil diameter would not matter. That prediction has implications for the brightness of images formed by lenses of different focal lengths that are not consistent with observations and measurements.

I will ask again, what is there in my earlier post (the one with the numbered statements) that you specifically object to?

Dec 10, 2012 at 07:10 PM
HelenB
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 p.7 #10 · p.7 #10 · silly inverse square law question.

Guari, reflecting surfaces do not have to behave as point sources for the inverse square law to apply to the energy flux governing the brightness of an image of that surface. The classic treatment of image illumination vs distance treats the object surface as a real surface. Surely you have seen that treatment? I can easily go through it here if you wish.

My numbered post above treats the object surface as having real area. What statement of mine, in that post, do you take exception to and why?

Dec 10, 2012 at 07:16 PM

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PeterBerressem
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 p.7 #11 · p.7 #11 · silly inverse square law question.

We (as well a the camera) receive nothing but the rays that are emitted from the subject at zero angle, resp. only the direct light rays. All light rays which are strayed by the subject are not relevant to us, no matter what distance.

Dec 10, 2012 at 07:17 PM
HelenB
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 p.7 #12 · p.7 #12 · silly inverse square law question.

The thing is that we do see divergent rays, and although the divergence angles can be extremely close to zero, they are significantly non-zero. They may seem tiny angles to us humans, but they are very important to the inverse square law. Those of you who say that the inverse square law does not apply have a real problem with conservation of energy - and that problem goes away when you consider that the energy flux is constant for constant solid angle.

It really is simple: objects appear to maintain their brightness regardless of distance because the inverse square law applies, and it is exactly offset by image magnification.

Dec 10, 2012 at 07:34 PM
RustyBug
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 p.7 #13 · p.7 #13 · silly inverse square law question.

Maybe we should discuss centripetal force instead?

Edited on Dec 10, 2012 at 08:11 PM · View previous versions

Dec 10, 2012 at 07:40 PM
BrianO
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 p.7 #14 · p.7 #14 · silly inverse square law question.

HelenB wrote:
The thing is that we do see divergent rays, and although the divergence angles can be extremely close to zero, they are significantly non-zero.

The problem is that the inverse-square law applies when light is radiated outward radially in three-dimensional space from a point source. While there may be some light spread to the reflected light that we see/capture, it is no longer enough to be described by the Inverse Square Law. The amount of dispersion can vary significantly depending on the shape, surface texture, and material make-up the subject. That's why we need light meters and not measuring tapes to read reflected light, whereas we can use tape measures (once we have a baseline to work from) to determine fall-off from a light source.

Re-read RDKirk's posts; he has it correct.

Dec 10, 2012 at 08:02 PM
HelenB
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 p.7 #15 · p.7 #15 · silly inverse square law question.

The inverse square law applies to reflected light from an object when that object is being imaged. It applies because conservation of energy applies. If it doesn't apply, there is a problem with conservation of energy. Why is this so hard to grasp? Once again, please tell me which of my previous numbered statements you disagree with. I've already explained what is wrong with RDKirk's post.

In general, when we say 'x behaves like y' we need to be very clear about the assumptions we made to arrive at that similarity, and hence the conditions under which it is applicable or not. Similarities that might be useful in one circumstance may not work in another. Approximations may work for some purposes, but that doesn't mean that they always work.

Dec 10, 2012 at 08:28 PM
BrianO
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 p.7 #16 · p.7 #16 · silly inverse square law question.

HelenB wrote:
The inverse square law applies to reflected light from an object when that object is being imaged.

If the light is collimated, or nearly collimated, or anything less than equally distributed in all directions, then the amount of fall-off is no longer inversely proportional to the square of the distance. Plus, we don't photograph point subjects, so we have reflected light from multiple virtual point sources falling on the imaging plane at the same time.

Dec 10, 2012 at 08:41 PM
RustyBug
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 p.7 #17 · p.7 #17 · silly inverse square law question.

If you divide an angle in half ... does it matter how long the rays that make up the angle are. The answer is of course "No." Neither does it matter if you move the camera a longer distance along the same path (i.e. on axis) as the closer distance ... the angle of incidence remained the same for a given object/surface angle), thus the angle of reflectance remained the same.

Those photons that emitted from the PLS ... AND ... are striking at an angle off of the object to be reflected IN THE DIRECTION OF the camera/eye will continue on that path to infinity, except as acted upon by an outside force.

Moving your light source closer to the object WILL put more photons on the object to be reflected because of the distance/angles associated with the ISL relationship from the PLS.

But, whatever volume of photons are put on the object to be reflected at the necessary angle to be contained within the angles of inclusion for capture ... THAT volume (1 baseball, 3 baseballs or all 20 baseballs) of photons will be reflected in accordance with AI=AR. Those then reflected photons will continue on that path ... iaw with Newton's First Law of Motion. The distance that they travel after being reflected, essentially collimated to the capture area in conjunction with AI=AR, does not cause them to lose energy, and the fact that the angles of inclusion predicated by AI=AR has already established WHICH photons are being sent along that (significantly) STRAIGHT path to the camera.

Edited on Dec 10, 2012 at 09:27 PM · View previous versions

Dec 10, 2012 at 08:50 PM
HelenB
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 p.7 #18 · p.7 #18 · silly inverse square law question.

If what you guys believe is true, then images would get brighter as you got further from the object, so not only would you fail to conserve energy but you would also break the second law of thermodynamics.

There seems to be a lot of confusion between the energy flux of an extended source as a source of light and the energy flux of an object being imaged.

Dec 10, 2012 at 09:00 PM
BrianO
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 p.7 #19 · p.7 #19 · silly inverse square law question.

HelenB wrote:
If what you guys believe is true, then images would get brighter as you got further from the object...

Where did you come up with that ridiculous idea; we never said anything that would indicate that.

Dec 10, 2012 at 09:21 PM
RustyBug
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 p.7 #20 · p.7 #20 · silly inverse square law question.

HelenB wrote:
If what you guys believe is true, then images would get brighter as you got further from the object, so not only would you fail to conserve energy but you would also break the second law of thermodynamics.

So now you're saying ... that we're saying ... a single photon gains energy as it travels? Which is it:

Without being acted upon by an outside force ...

A) a photon gains energy as it travels
B) a photon loses energy as it travels
C) a photon's energy remains constant as it travels in accordance with Newton's First Law of Motion

Dec 10, 2012 at 09:28 PM
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