Really stupid physics question

[pgriz]

figured that this one would be too easy for Helen B. She is a world of knowledge, that it undeniable.

And who also manages to suffer the fools among us and not get unhinged. Another plus.

 

[unpopular]

Oh but when she does it is very, very impressive ....

 

[pgriz]

Ah yes, I remember that incident. Made a mental note NOT to pick a fight with HelenB. There's just no win in that.

 

[tris_d]

No need, Helen adequately answered the question. Thanks Helen, as usual you're explanations are concise and clear.

Then if you took a telephoto lens, would exposure time be shorter with a wide angle lens under similar magnification (i.e. closer to the subject), provided that the f-ratio stayed constant?

OK, but I had already sent the email -- so what the heck, here's his answer.
My son teaches physics at the Univ. MN and is a Phd candidate working in bio-physics (proud dad here).

Joe

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The inverse square law is true for a light source that is a point - infinitely small. More precisely, the inverse square law is an approximation that is valid if you're far enough away from the light source that the physical extent of the source is negligibly small. So if you have a small flash, say 1 square centimeter, and you're 10ft from it, the inverse square law will give you reasonably accurate results. If you have a larger source, and you're not super far away from it, then you're dealing with something more complicated.

You can think of the large source as being composed of many dim point sources. (You can build something like a light box by gluing 500 small LEDs onto a piece of plywood.) Mathematically, to derive the "modified" inverse square equation, you would add up (integrate) the intensity contribution from each little light bulb. We know that the contribution from each little bulb is = (bulb intensity)/r^2, where r is the distance from a light bulb to the point you place your exposure meter. r is different for EACH little bulb. After doing the geometry and the integral, you will end up with an equation that depends on how far you are from your light box and the shape of the light box (ie, circle, triangle, rectangle, etc). Most light boxes have lengths that are approximately the same as their height (3' x 4'), so we might approximate all light boxes as something simple like a circle or a square. We can then express our approximate formula in terms of the surface area of the light box.

One interesting note: If you have a spherical light source (like one of those oriental paper lanterns), it still follows the inverse square law no matter how close you are to it. You can think of this as a quirk peculiar to spheres. Of course, this isn't going to be too interesting to photographers since most light boxes you'd encounter in a studio have flat surfaces.

Isaac

- "If you have a spherical light source (like one of those oriental paper lanterns), it still follows the inverse square law no matter how close you are to it. You can think of this as a quirk peculiar to spheres."


Did this guy just say that spherical light source if photographed from, say two meters away, will look not only smaller, but would also be four times less bright than when photographed from one meter away?

 

[christop]

Did this guy just say that spherical light source if photographed from, say two meters away, will look not only smaller, but would also be four times less bright than when photographed from one meter away?

No.

 

[tris_d]

Did this guy just say that spherical light source if photographed from, say two meters away, will look not only smaller, but would also be four times less bright than when photographed from one meter away?

No.

What then? What else could he mean by "follows the inverse square law"?

 

[unpopular]

light is focused to to a smaller region proportional to it's distance. This is why it's relative brightness appears similar and unaffected by distance - because our eyes and cameras alike have lenses that focus the light. What that light illuminates does not focus it, this is why inverse square appears to apply to ambient illumination, and directly imaged - such as the candle illustration you had in your other threads. The more distant, the smaller the projection and more densely distributed. Unfocused, the light falls off by inverse square as expected.

It's hard to imagine, because we always assume that light is packaged into nice little bundles that are easily determined from one another. This isn't how light behaves - we've developed lenses so that we can determine objects. We think of a cameras lens as a sort of artificial aid to make light behave as it "truly is". But light in it's natural form is just ambient radiation, scattering out in all directions. It's not focused into neat little packets and projected into distributions relative to distance, simply because we need it to.

All light follows inverse square. Lenses just take that dispersed light and focus it back into a representation of the source. Light radiates off the source by emission or reflection, spreads out according to inverse square, some portion of it enters the lens and is focused back down to a region we call "bright": a relatively dense region of photons.

In fact, if the back focus distance is too great, you again loose brightness. In photography (since ypu're clearly not a photographer), this is compensated by a bellows extension factor.

 

[tris_d]

light is focused to to a smaller region proportional to it's distance. This is why it's relative brightness appears similar and unaffected by distance - because our eyes and cameras alike have lenses that focus the light. What that light illuminates does not focus it, this is why inverse square appears to apply to ambient illumination, and directly imaged - such as the candle illustration you had in your other threads. The more distant, the smaller the projection and more densely distributed. Unfocused, the light falls off by inverse square as expected.

It's hard to imagine, because we always assume that light is packaged into nice little bundles that are easily determined from one another. This isn't how light behaves - we've developed lenses so that we can determine objects. We think of a cameras lens as a sort of artificial aid to make light behave as it "truly is". But light in it's natural form is just ambient radiation, scattering out in all directions. It's not focused into neat little packets and projected into distributions relative to distance, simply because we need it to.

All light follows inverse square. Lenses just take that dispersed light and focus it back into a representation of the source. Light radiates off the source by emission or reflection, spreads out according to inverse square, some portion of it enters the lens and is focused back down to a region we call "bright": a relatively dense region of photons.

In fact, if the back focus distance is too great, you again loose brightness. In photography (since ypu're clearly not a photographer), this is compensated by a bellows extension factor.

Interesting. Ok, thank you. That's whole another thing to consider now, I wish you mentioned it before.

 

[unpopular]

*blink* it was THIS thread that explained it to me!

 

[Fred Berg]

Oh lord, this inverse square law is difficult. What I learnt last time this came up (and is useful and relevant to me) is, the larger an object is the more light (or time) you need to properly expose it. Is this why when you zoom out in A mode the shutter time speeds up? Zoom in to 70mm on an ornament from 3 meters away: 1/60 , zoom out to 35mm: 1/250. This didn't come directly out of the last discussion, but this is what I boiled things down to after scratching my head and digging around in various books. Otherwise, the only real use for this law seems to be when working out how much drop off there will be when using flash.

If I wasn't tea-total, I'd pour myself a stiff drink whilst trying to get to grips with this.

 

[christop]

What I learnt last time this came up (and is useful and relevant to me) is, the larger an object is the more light (or time) you need to properly expose it.

I don't know how you came up with that idea. It doesn't make any sense.

Is this why when you zoom out in A mode the shutter time speeds up? Zoom in to 70mm on an ornament from 3 meters away: 1/60 , zoom out to 35mm: 1/250.

More likely you included brighter objects in the frame when you zoom out (such as lights) which causes the auto metering to speed up the shutter speed to compensate. Or the auto metering chooses a wider aperture at 35mm than at 70mm. Inexpensive zoom lenses have variable maximum aperture: my 18-50mm lens ranges from f/3.5 at 18mm to f/5.6 at 50mm, for example. This is about 1.3 stops difference.

 

[runnah]

Nice try photography...you almost made me learn physics.

 

[tris_d]

*blink* it was THIS thread that explained it to me!

All I see is they told you, like they told me, that things appear four times smaller at double the distance and that is supposed to explain inverse square law, which it does not. Now, while your explanation with focusing makes sense I don't see how focus could compensate for a light that is supposed to appear four times dimmer at double the distance or sixteen times dimmer at quadruple the distance. Also I could get that you can focus one light source, but how in the world could you focus on many light sources at once, like on that image with street lights.

Looking back at christop's light bulbs I could say now the further one does not look dimmer because the light source is not spherical, but the filament is cylindrical, so inverse square law was not to be expected. However, if we were to look at ambient (walls) around that light bulb we would expect to see inverse square law drop off as you explained, so I still can't make sense of it. -- I wish we could summon Isaac to shed some more light on the subject. Ysarex, you there?

 

[amolitor]

*blink* it was THIS thread that explained it to me!

All I see is they told you, like they told me, that things appear four times smaller at double the distance and that is supposed to explain inverse square law, which it does not.

You are precisely and exactly wrong, here. Lest someone stumble across this and become confused, let me be quite clear: Tris is wrong on this point. Things appear 4 times smaller at double the distance, and that is exactly the explanation for the inverse square law.

 

[fjrabon]

You are precisely and exactly wrong, here. Lest someone stumble across this and become confused, let me be quite clear: Tris is wrong on this point. Things appear 4 times smaller at double the distance, and that is exactly the explanation for the inverse square law.

It's like you think he finally gets it, and then all of the sudden we are back at square one.