# Concerning Inverse Square Law

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### #1 Jonathan Wilcox

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Posted 08 April 2011 - 07:18 PM

Does the inverse square law apply to all lights? Including diffusion panels, chimeras, fresnels, pars, source 4, natural daylight coming from a window, etc.?

Does the law change at all when dealing with lights such as Pars (that are supposed to have longer throw capabilities?) What does 'throw' have in relation to inverse square law.

And in what situations would you use a light with more throw and in what situations would you use a light with less throw?
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### #2 Chris Millar

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Posted 08 April 2011 - 08:00 PM

It refers to point sources only - in infinitesimally small point of light - which no light is... Lights are an integration of many points of light all projecting their own spheres of transmission, creating a kind of 3 dimensional offset paths to fuddle up your dinner party arguments.

But all lights tend towards point sources the further you get away from them, and you don't need to be too literal with it as the adjustment required to get it right is both waaaaaay too complex to figure out and also well within the range of errors conjured up by every other factor involved.

But yes, if you are very close to a large wall of very bright end even diffusion the inverse square law will not apply so perfectly.
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### #3 Jonathan Wilcox

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Posted 08 April 2011 - 08:08 PM

It refers to point sources only - in infinitesimally small point of light - which no light is... Lights are an integration of many points of light all projecting their own spheres of transmission, creating a kind of 3 dimensional offset paths to fuddle up your dinner party arguments.

But all lights tend towards point sources the further you get away from them, and you don't need to be too literal with it as the adjustment required to get it right is both waaaaaay too complex to figure out and also well within the range of errors conjured up by every other factor involved.

But yes, if you are very close to a large wall of very bright end even diffusion the inverse square law will not apply so perfectly.

Yeah makes a lot of sense. I was doing a test with a light meter and a large soft source and the numbers were way off from the inverse square law equation.
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### #4 Chris Millar

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Posted 08 April 2011 - 11:56 PM

I'm coding some stuff in Maya at the moment to do with volumetric displays and some of the issues that cropped up got me thinking about it just the other day actually, funny your question should crop up!

I'm going to figure out the radiation fall off for a sensor that is moving away from an infinite plane of even light (in a perpendicular direction) - then a plane with boundaries (i.e. a softbox) and then after that tackle what I'm assuming will be a harder equation of the fall off for a diffuse sphere (even though the sphere is getting smaller as you get further away, you are seeing more and more of its 'sides')...

Maybe then throw in some mathematically defined falloffs within the effect of diffusion to simulate the hot spots of the filaments etc...

In code it wont need to be so full on as you get the dial in the resolution of the summations that are integrated. Ha ha, I'll get around to it one day I'm idle at work and post results
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### #5 John Sprung

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Posted 09 April 2011 - 12:51 AM

Inverse square applies to point sources. To figure out larger sources, just treat every point on the larger source as an individual point source, and do a double integral over the area of the source. Reflection from real world surfaces isn't perfectly diffuse, so you may want to multiply by a weighting function of the angle for bounce light. Of course in the real world you have bounce light all over the place from everything, adding back into what you calculate from your theoretical source. The SIGGRAPH types call this stuff "Radiosity".

OTOH, you could just use a light meter.

-- J.S.
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### #6 Hal Smith

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Posted 09 April 2011 - 02:37 PM

Inverse Square Law (1/D^2) applies to point sources as noted above. An infinitely large source follows Inverse Law (1/D). Sources in size between the two are neither 1/D^2 or 1/D but somewhere between the two. When Cinematographers talk about "fall-off" being different for different light sources that's what they're talking about. A physically small source like an open face fixture has Inverse Square behavior and a fast fall-off. Conversely a large extended source like a 10X10 diffusion frame with it's subject relatively close is approaching Inverse Law and has a slow fall-off. That's why if you want a close up that has dramatic shadows you use a small source and if you want a "Beauty Shot" you use large diffused sources.

Light an aging actress with a Blonde and no fill (all Inverse Square Law lighting) and she'll never want you anywhere near her again. But use a large book light (approaching perfect Inverse Law), a little hair light, and a bit of diffusion and she'll think you're the greatest Cinematographer to ever walk the face of the earth.
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### #7 Ronald Gerald Smith

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Posted 09 April 2011 - 03:36 PM

Inverse Square Law (1/D^2) applies to point sources as noted above. An infinitely large source follows Inverse Law (1/D). Sources in size between the two are neither 1/D^2 or 1/D but somewhere between the two. When Cinematographers talk about "fall-off" being different for different light sources that's what they're talking about. A physically small source like an open face fixture has Inverse Square behavior and a fast fall-off. Conversely a large extended source like a 10X10 diffusion frame with it's subject relatively close is approaching Inverse Law and has a slow fall-off. That's why if you want a close up that has dramatic shadows you use a small source and if you want a "Beauty Shot" you use large diffused sources.

Light an aging actress with a Blonde and no fill (all Inverse Square Law lighting) and she'll never want you anywhere near her again. But use a large book light (approaching perfect Inverse Law), a little hair light, and a bit of diffusion and she'll think you're the greatest Cinematographer to ever walk the face of the earth.

Are you talking about fall-off - how the light falls off of the edges, or are you talking about how fast the light gets darker as you move away from the light? There seems to be two ways that people talk about fall-off. Once and for all, what is the absolute correct way to use the term 'fall-off'?
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### #8 Chris Millar

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Posted 09 April 2011 - 04:58 PM

Maybe there is a strict film lighting term for fall off but I'm referring to the nature of things 'falling off' as 'fall-off', another example is a lighting fade over time, that also has a fall off - go figure
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### #9 Hal Smith

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Posted 09 April 2011 - 05:37 PM

Are you talking about fall-off - how the light falls off of the edges, or are you talking about how fast the light gets darker as you move away from the light? There seems to be two ways that people talk about fall-off. Once and for all, what is the absolute correct way to use the term 'fall-off'?

Don't tempt me to pontificate about "Umbra/Penumbra/Antumbra".

But if you peek into Wikipedia you'll start to get the idea.
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### #10 Ronald Gerald Smith

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Posted 09 April 2011 - 06:38 PM

Don't tempt me to pontificate about "Umbra/Penumbra/Antumbra".

But if you peek into Wikipedia you'll start to get the idea.

Thanks Hal, the wikipedia page here http://en.wikipedia.org/wiki/Umbra is quite brief but very interesting. I'm going to look further into this....
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