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# Thread: Inverse square law, sort of...

1. ## Inverse square law, sort of...

Let me preface this by saying that it's past 4 am (late to bed, not early riser), I can't quite think of the answer, and it's unimportant enough that I will forget it the next day. But, it's a curious thought...

(1) Inverse square law states that light will fall off exponentially (the equation doesn't matter for the purposes of this discussion--or does it?!).
(2) The camera records light that is reflected off of the subject.
(3) Light rays travel from source to subject, then bounce off the subject, then into the camera. The light travels the distance of D_total = D_source-to-subject + D_subject-to-camera.
(4) Assume the source and subject remain at a constant distance from each other.
(Q) Shouldn't changing the distance between subject and camera change light intensity (via inverse square law), since the light has to travel that much more/less? Let's say we have a properly exposured photo at X distance from subject. Why does changing subject-to-camera distances, by X/2 or 2X, require no stop-compensation?

2. Yes, but as you increase the camera to subject distance, the area the subject occupies on the film reduces by the same ratio so the light density remains the same.

Steve.

3. Originally Posted by Steve Smith
Yes, but as you increase the camera to subject distance, the area the subject occupies on the film reduces by the same ratio so the light density remains the same.

Steve.
Using a constant-aperture zoom lens to keep composition the same, while changing distance. You'd still use the same shutter speed.

4. Think of it more in terms of glass and apertures than film.
Say you're somewhere where you need 400mm to fill the frame with the subject, the aperture according to the light is f/4, 100mm diameter.
Then move a bit closer, you need 50mm to fill the frame. You still need f/4 for the light, but now that means 12.5mm diameter.
Move closer, smaller 'light gathering area' ie the aperture. Square law. Yeah.

5. The inverse square law works for light falling on the subject; not reflected light from the subject, which is not a point source.

6. At practical distances individual light "rays" can be thought of as not changing in intensity.

As light moves toward a subject from the light source, the "rays" spread out.

Lets say that at a distance of 1X the measured luminance might be 1 and a given set of rays might cover an area of 1.

At a distance of 2X the light has spread out and the same number of rays now cover an area 4 times larger.

So a light meter's sensor has a fixed size, lets call it 1. So at a distance of 1X the meter will measure a certain amount of light rays.

At a distance of 2X the light has spread out, but the meter hasn't. The meter area still equals 1, but now the area the light covers equals 4. So the meter will only see 1/4 of the light rays it saw before. Just like the meters sensor, there are only 1/4 of the light rays available to be bounced back from a given size subject, at that distance, toward the camera.

What the meter sees at that distance will give the right info needed to decide on the right exposure for that subject. Remember that individual light rays don't diminish.

The same thing does though happen going back the other way but it is easier for me to think about this as the size and importance of the subject matter in the composition changing (the subjects size on the film).

7. I think the at different object camera distance the inverse square law is simply compensated by the size of the object on the film:

If we double the distance between camera and object 1/4 of the light arrives at the film plane but the object has now half of the size on the film plane. Hence the object has 1/4 of the area on the film plane and the light energy per film area is constant.

8. Originally Posted by cowanw
The inverse square law works for light falling on the subject; not reflected light from the subject, which is not a point source.

Exactly. If the inverse square law worked for reflected light, the whole world would be dark.

9. Originally Posted by jcc
Using a constant-aperture zoom lens to keep composition the same, while changing distance. You'd still use the same shutter speed.
Correct, but the light collecting area of your lens would increase as you moved away from the subject, making up for the effect of the inverse square law fall-off of the light.

For example, suppose you stand 4m from the subject with a 40mm f/4 lens. The diameter of the lens aperture is 40mm/4 = 10mm.

Now you move 12m away and zoom to 120mm, still f/4, to keep the same framing. Now the clear aperture diameter is 120mm/4 = 30mm.

Although the f-stop remains the same, the actual diameter of the aperture opening has increased by a factor of 3 and the light gathering area, which is proportional to the square of the diameter, increases by a factor of 9.

At the same time since you are now 3 times further away from the subject, the light falling per unit area has reduced by a factor of 9 due to the inverse square law.

However since the effective light gathering area of the lens has increased by the same amount, these effects cancel out and the amount of light reaching the sensor (and hence the required exposure) remains the same.

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10. Originally Posted by cowanw
The inverse square law works for light falling on the subject; not reflected light from the subject, which is not a point source.
Actually it is also applicable to reflected light. If the light is coherently reflected, for example by a mirror, then the fall-off follows the inverse square law for the total path length (source to reflector + reflector to observer).

If it is scattered, for example by illuminating a non reflective subject, then the subject acts like a whole lot of point sources and the law applies twice - once to the distance from source to subject and once for the distance from the subject to the observer.

(This is similar to the so-called radar range equation, which states that the reflected power received from a target decreases with the fourth power of distance since the inverse square law applies separately to the transmitted and reflected wave paths.)

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