Physics/Optics Question - Please Help

[Kanastrous]

So right now there's a thread going on a digital-video production site I frequent regarding the physics of light and the inverse-square law. I'm hoping someone with the physics background to clarify the issue being discussed will take a minute or two to look through the thread (from the page linked below onwards) and set us straight, because we're all coming up with different ideas and none of us have the grounding in physics to make an explanation stick.

http://www.dvxuser.com/V6/showthread.ph ... 858&page=2

Thanks in advance for taking some time to educate us over there...

[Samuel]

I don't have a phsycis background however... are the denying the inverse square law for reflected light?

If you have a beam of light directed you don't experience fall off (aside from atmosphere and leaking), if it is broadcasting in all directions you are subject to the inverse square law.

[Kuroneko]

I haven't read closely into the thread, and I'm not a physicist, but I did have an interest in the perception of light, and in particular questions of the following sort: given such-and-such power spectrum, (a) what color is it, and (b) how bright is it? (It started with a blackbody of a given temperature, and I got around to writing some MATLAB code interpolating some luminosity tables from other sources.)

It's true that the emitted power falls off as 1/r² from the source. For reflection, there will be a kind of two-step process: 1/r² from the source to the object and another 1/R² from the object to the detector (cf. radar equation). If the source and detector are the same--say, a camera with a flash that provides most of the illumination--then this is a total of 1/r4. One can talk about these two steps as separate, treating the reflecting object as if it was a source; this is absolutely not a problem as long as one is clear about it is meant.

Part of the confusion in that thread, it appears to me, is an equivocation between what corresponds to luminous intensity and luminance.

Luminous intensity is simply the power of the source weighted according to some luminosity function. The way this works is that because human eyes have different responsiveness to light of different wavelengths/frequencies, lights of the same subjective brightness may have correspond to different physical power depending on the wavelength/frequency of the light. It's actually a bit more complicated than that, because there are four structures in the human eye, each of them having their own contribution: there 'photopic' (when cones are important, bright light) luminosity functions and one 'scotopic' (when monochrome rods dominate, in low light), and further even individually they may even have some variations depending on the conditions.

Luminous intensity is the same, independent of distance, for a given light-source, e.g., a lightbulb. One can think of it as how much brightness it puts out "in total." On the other hand, luminance is luminous intensity per area, and this is what changes--e.g., a light bulb far away won't be as useful in illuminating things compared to if it was nearby. One can think of luminance as how much brightness a source puts "over here."

What complicates things is when you start taking geometry into account. The most obvious is if the light-source is non-isotropic (e.g., a flash puts light in the front) The inverse-square law still applies int he sense that for any fixed direction, luminance in that direction falls off as 1/r², but it is now also a function of direction, which makes a difference both in relative orientations and in how the light reflected (cf. Lambert's law, which is a good approximation). Additionally, the speed of light is so great that you generally won't have just one reflection to consider, and not just reflection from the object (but also, say, source->floor/etc.->object).

If you have a beam of light directed you don't experience fall off (aside from atmosphere and leaking), if it is broadcasting in all directions you are subject to the inverse square law.

That's not quite true. Unless the beam is collimated to absolute perfection, it's still the case the given a particular direction, the power per area falls off as 1/r² (e.g., think of a cone). It's just now it is also a function of direction as well.

[Fingolfin_Noldor]

Utter rubbish. Any incoherent light is subject to inverse square law. Worse still is that unless it is a dielectric mirror (meaning multiple alternating layers of dielectric coating), any light or electromagnetic wave will be absorbed to some extent!

[Feil]

What we perceive as brightness is light flux. Light flux is defined as the surface brightness or "source intensity"* multiplied by the apparent (angular) area. Source intensity is the power per unit area at the source. Apparent area decreases according to the inverse square of the distance: a person twice as far away takes up half the width and half the height in your vision, which is 1/4 the area; a person five times as far away takes up 1/5 the width and 1/5 the height, which is 1/25 the area, and so on.


Source intensity is constant for a primary light source and, obviously, variable for a secondary light source (i.e. if the moon was a trillion miles further from the sun, it would have very low source intensity and you wouldn't be able to see anything even if you were standing on it).

In the case of a person retreating from a camera flash in the same place as the observer (which in this case is the film), the intensity of the light source falls off according to the inverse square of the distance. Think back to the moon example. If we teleported Earth and Moon a trillion miles away from the sun, would you say that the moon would still be as bright? Of course not. Similarly, the intensity of light reflected from the person walking away from the camera flash decreases according to the inverse squares law.

Because the angular size of the individual decreases according to the inverse square of distance also, the light flux, which is intensity multiplied by apparent area, varies according to k/x^4 where x is distance and k is a constant such that if angular size varies according to a/x^2 and intensity varies according to b/x^2, k = a*b.

Experiment if you doubt the truth of this: Place a flashlight beside a mirror in an open field or very large room. Direct another identical flashlight at the mirror and walk away from the mirror. Observe which light - the stationary flashlight or the reflected flashlight - becomes dimmer at the faster rate.


*surface brightness is the term used in astronomy, if I recall correctly. I don't know if anybody but me uses "source intensity", but what we're measuring is the intensity at the surface and "brightness" is an abstract term with no associated units, so I prefer to use a term that makes sense with the rest of the study of physics.

(Note: sometimes people talk about the intensity of light from distant stars or other objects decreasing with their distance. They are using intensity to mean the intensity of light AT THE OBSERVER, not source intensity, which is the intensity of light at the source and is constant for a lightsource.)


EDIT: Obviously, this only applies to cameras if the light on the subject is FROM THE CAMERA. If you are photographing someone illuminated by sunlight or lots of indoor lights creating a high ambient light level, then their source intensity is constant because the amount of light shining on them stays the same. In this case their light flux only decreases according to 1/x^2, not 1/x^4. Therefore the per-unit-area brightness observed by an observer (or, to use different words to describe the same thing, the amount of exposure on the film of the image being captured) does NOT vary with distance if the observed object is lit at an unchanging level as by sunlight or indoor lights.

[starslayer]

*surface brightness is the term used in astronomy, if I recall correctly. I don't know if anybody but me uses "source intensity", but what we're measuring is the intensity at the surface and "brightness" is an abstract term with no associated units, so I prefer to use a term that makes sense with the rest of the study of physics.

The correct term here is exitance. W/m^2 of light falling on a subject is the irradiance. And yes, surface brightness is used in astronomy when speaking about diffuse objects, and is given as a magnitude.