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Inverse-Square Law?

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The "simple" math is based on a point source. In most cases, the relative size of the light is small enough that for any practical purpose that can be considered a point source.

I don't claim to understand the math behind this but the effect is easy enough to replicate and measure.

However with very large light sources (relative to the subject) the light does not fall off by the inverse square. Imagine lighting an grape with a 24" softbox from 6" away. The inverse square law would predict 25% as much light at 12" compared to the amount at 6". This is not what happens. The light falloff is significantly less. The amount of light at 3" should be 4x that of 6" but again, it is not.

In close-up photography and marco photography, the light source may well be larger than the subject. A bare speedlight is huge compared to an ant a foot away.

I think once the light source is the same size or smaller than the subject, it can be thought of as a point source and the inverse square law will accurately predict the light fall-off.
Quantum Help said:
Photocelluite:

The Inverse Square law is a matter of pure physics. It is a mathematical progression, plain and simple. It does not matter where the light is coming from: ie, a bare bilb, a flash head with reflector, an umbrella, a softbox, or a plain match stick. It is mathematics.

For example at 5 feet a light produces f/16. 5 x 16 = 80. That is the guide number

go to the next double of 5, which is 10. No light meter needed, just math. Guide number of 80 divided by 10 feet = f/8.

Double the 10 feet for the next step 10 x 2 = 20 feet. Guide # of 80 divided by 20 = f/4.

Simple math, nothing else.

The softbox, which is closer, will produce more light only because it is closer. It will also offer a wrap around lighting effect because of the closeness and size of it. Move it farther back, it will lose light because of the inverse square law and will also lose the soft wrap around effect because the farther away you move it from the subject, the more it will become a point light source.
Click to expand...
--
-Dan Rode
http://rodephoto.com
 
yOOrek said:
I still don't get it. What about zooms? I can increase the distance to the subject, zoom in, therefore increasing the size of the image on the sensor, and still keep the same exposure settings. There must be something fundamental I'm missing here.

Let's take the studio setup as an example. I take the incident reading at the subject that gives me, let's say f8 @ 1/250. Then no matter how far or how close I am to the subject, how much I zoom in or out, the face will be exposed the same.
OK it's 3am here and my thinking might be slow. :-)
Click to expand...
Light fall off is light fall off. Bulb to subject and subject to camera.

An evenly overcast day or open blue sky are nice large light sources. Take your favorite zoom lens and at its widest focal length, Meter a F8 image of the sky and then while keeping an eye on your meter, zoom in to your longest focal length.

See?

(the same can be done with an evenly lighted wall)

--
(insert brag sheet here)
http://flickr.com/photos/mbloof
http://www.Marko-Photo.com
Technologist @ Large
  • Mark0
 
Quantum Help said:
Photocelluite:

The Inverse Square law is a matter of pure physics. It is a mathematical progression, plain and simple. It does not matter where the light is coming from: ie, a bare bilb, a flash head with reflector, an umbrella, a softbox, or a plain match stick. It is mathematics.

For example at 5 feet a light produces f/16. 5 x 16 = 80. That is the guide number

go to the next double of 5, which is 10. No light meter needed, just math. Guide number of 80 divided by 10 feet = f/8.

Double the 10 feet for the next step 10 x 2 = 20 feet. Guide # of 80 divided by 20 = f/4.

Simple math, nothing else.

The softbox, which is closer, will produce more light only because it is closer. It will also offer a wrap around lighting effect because of the closeness and size of it. Move it farther back, it will lose light because of the inverse square law and will also lose the soft wrap around effect because the farther away you move it from the subject, the more it will become a point light source.
Click to expand...
It seems photographers (me included) like to throw the inverse square law around a bit :). However, the inverse square law holds true only for a point light source with divergent rays; In other words, a source without benefit of control by a reflector. One example that pretty well follows this definition is a candle flame.

Should the light rays be parallel or converging, then the law is not applicable. An example of a parallel beam would be a searchlight or spotlight, where illumination is almost independent of the distance between the light source and object, except for that portion of the beam lost to absorption by the intervening atmosphere.

Now the good part:

The law in the strictest sense does not apply to common lighting tools used by a professional photographer. Often these tools use a curved reflector or broad sources of diffused light such as umbrellas, bank lights, and tents. The light in these types of sources are usually emitted in arbitrary, random bundles such as to resist the law. (Some of the newer products tend to make the light rays more parallel then others).

Practically speaking photographers use the ISL as an indication of what the light source is doing in terms of light fall-off. In general, it is close enough for most photographers’ work. However, depending on the particular light source used there often will be a difference between the calculated and actual measured values.

The inverse square law does have validity when applied to light projected from a photographic lens, as the lens optical center is considered a point light source.

--

I once had a perfectly exposed image of a white cow in a snow storm eating marshmallows.
 
Good point.

Point sources will drop off as an inverse square. Line sources (like being close in to a tube light) will be just the inverse (1/r). There are assumptions in there like a point source being a true point which is not possible. If you are close in, the source looks like an area, and the near field falloff rate will be lower.
DRode said:
When working with large softboxes and umbrellas very close to the subject, one will lose much less than the inverse square. I don't know the math behind why this is the case but that's how it works.
photocellulite said:
What are they talking about in this video, twice the distance equals 1 f-stop?

http://lightenupandshoot.blogspot.com/2010/05/depth-of-flash-exposure-aka-inverse.html#comments
Click to expand...
--
-Dan Rode
http://rodephoto.com
Click to expand...
 
ProTL said:
Should the light rays be parallel or converging, then the law is not applicable.

An example of a parallel beam would be a searchlight or spotlight, where illumination is almost independent of the distance between the light source and object, except for that portion of the beam lost to absorption by the intervening atmosphere.
Click to expand...
Here you make the classic point very clearly, but I don't think it is as certain as you say. I can give a ready example where it just isn't true... which is why I try not be too prescriptive about the Inverse Square Law not working with focused beams.
ProTL said:
Now the good part:

The law in the strictest sense does not apply to common lighting tools used by a professional photographer. Often these tools use a curved reflector or broad sources of diffused light such as umbrellas, bank lights, and tents. The light in these types of sources are usually emitted in arbitrary, random bundles such as to resist the law. (Some of the newer products tend to make the light rays more parallel then others).
Click to expand...
Okay. My example:

The light from camera top flashguns and hammerheads is formed up by an optical system that is pretty much identical to that of a standard Fresnel spotlight...

.... that is, with a flattened Fresnel type lens in front of the light source, and a mirrored parabolic reflector behind it. Zoom head flashes even flood/spot the beam in precisely the same way as full-size Fresnel spotlights, by moving the lightsource and mirror assembly nearer (flooded) and further (spotted) to the lens.....

... and yet camera-top flashes conform very closely indeed to Inverse Square Law, suggesting that these relatively small versions of Fresnel spotlights may be considered as point light sources, and that the fancy optical system isn't having much effect to counter the drop-off from ISL.

Note: The calculator dial of a conventional flashgun readily indicates that ISL is considered to apply, as does the provision of only ONE Guide Number for all distances, of course.

snip..
ProTL said:
The inverse square law does have validity when applied to light projected from a photographic lens, as the lens optical centre is considered a point light source.
Click to expand...
Errr.... does it?

If it does, it might explain why camera-top flashguns drop-off according to ISL. (see above) However, since what lenses produce is very much a focused beam , why is there insistence that Inverse Square Law only applies to point sources radiating without benefit of optical works like reflectors and lenses?

Is it just small size?

I mean, large reflectors for large studio flashes... they come with Guide Numbers, too, don't they....? I know that I have seen them quoted.

Further to the same point...

I have used very large flashbulbs [PF-100... seriously large] to shoot 5x4" Ektachrome in bulb-flash reflectors the size of a dustbin lid and firing up to five bulbs at once....

http://www.flashbulbs.com/Philips_ph-5.htm

.... and found that their published Guide Numbers held up pretty reliably. Be aware that Ektachrome, not being noted for massive exposure latitude, would have "let us know" if the exposures were wrong....!! (shrugs)

Softboxes up close we know are a different matter, but as far as focused light is concerned (and by whatever means it has been shaped up and headed in the same direction)......

.... I am suggesting that Inverse Square Law WORKS a lot more often than it don't. :-)
--
Regards,
Baz

"Ahh... But the thing is, they were not just ORDINARY time travellers!"
 
Barrie Davis said:
ProTL said:
Should the light rays be parallel or converging, then the law is not applicable.

An example of a parallel beam would be a searchlight or spotlight, where illumination is almost independent of the distance between the light source and object, except for that portion of the beam lost to absorption by the intervening atmosphere.
Click to expand...
Here you make the classic point very clearly, but I don't think it is as certain as you say. I can give a ready example where it just isn't true... which is why I try not be too prescriptive about the Inverse Square Law not working with focused beams.
Click to expand...
Yes, my example above is very narrowly interpreted in an effort to make the point. To suggest we all should rigorously enforce that example wasn’t my intention.
Barrie Davis said:
Barrie Davis said:
Now the good part:

The law in the strictest sense does not apply to common lighting tools used by a professional photographer. Often these tools use a curved reflector or broad sources of diffused light such as umbrellas, bank lights, and tents. The light in these types of sources are usually emitted in arbitrary, random bundles such as to resist the law. (Some of the newer products tend to make the light rays more parallel then others).
Click to expand...
Okay. My example:

The light from camera top flashguns and hammerheads is formed up by an optical system that is pretty much identical to that of a standard Fresnel spotlight...

.... that is, with a flattened Fresnel type lens in front of the light source, and a mirrored parabolic reflector behind it. Zoom head flashes even flood/spot the beam in precisely the same way as full-size Fresnel spotlights, by moving the lightsource and mirror assembly nearer (flooded) and further (spotted) to the lens.....

... and yet camera-top flashes conform very closely indeed to Inverse Square Law, suggesting that these relatively small versions of Fresnel spotlights may be considered as point light sources, and that the fancy optical system isn't having much effect to counter the drop-off from ISL.
Click to expand...
Here, my point again must be understood in the most absolute sense of the definition. To quote myself above I say “in the strictest sense” and to quote you, you say “conform very closely”, hopefully we agree.

I’m reminded about a recent post where the OP wanted to better understand why his calculation and measured values were not the same. I didn’t respond because I believed you answered his question accurately regarding point light sources. That is why I prefaced my statement with “depending on the particular light source used there often will be a difference between the calculated and actual measured values.” Often these small differences are not enough for most photographers to even consider or be aware of.
Barrie Davis said:
Note: The calculator dial of a conventional flashgun readily indicates that ISL is considered to apply, as does the provision of only ONE Guide Number for all distances, of course.

snip..
Click to expand...
Yes it works!
Barrie Davis said:
Barrie Davis said:
The inverse square law does have validity when applied to light projected from a photographic lens, as the lens optical centre is considered a point light source.
Click to expand...
Errr.... does it?
Click to expand...
Yes it does on this point.
Barrie Davis said:
If it does, it might explain why camera-top flashguns drop-off according to ISL. (see above) However, since what lenses produce is very much a focused beam , why is there insistence that Inverse Square Law only applies to point sources radiating without benefit of optical works like reflectors and lenses?

Is it just small size?
Click to expand...
I would suggest divergent rays. Your PF-100 flashbulbs can also be considered a point light source as well. That is, unless you put a shade on it thereby altering or conforming the light, similar to a candle flame.
Barrie Davis said:
I mean, large reflectors for large studio flashes... they come with Guide Numbers, too, don't they....? I know that I have seen them quoted.

Further to the same point...

I have used very large flashbulbs [PF-100... seriously large] to shoot 5x4" Ektachrome in bulb-flash reflectors the size of a dustbin lid and firing up to five bulbs at once....

http://www.flashbulbs.com/Philips_ph-5.htm

.... and found that their published Guide Numbers held up pretty reliably. Be aware that Ektachrome, not being noted for massive exposure latitude, would have "let us know" if the exposures were wrong....!! (shrugs)

Softboxes up close we know are a different matter, but as far as focused light is concerned (and by whatever means it has been shaped up and headed in the same direction)......

.... I am suggesting that Inverse Square Law WORKS a lot more often than it don't. :-)
Click to expand...
I agree, for me the ISL works all the time. I hope this isn’t a poor analogy but I’ll throw it out there and probably get eaten alive :) . Considering even the largest studios things are going to follow just as they always have. However, if we had to make precise calculations over large distances where the difference meant landing on the moon or missing our target we certainly would want to take into consideration how the lights rays are being modified. A good discussion Barrie
Barrie Davis said:
--
Regards,
Baz

"Ahh... But the thing is, they were not just ORDINARY time travellers!"
Click to expand...
--

I once had a perfectly exposed image of a white cow in a snow storm eating marshmallows.
 
Perhaps i am off base here, but even with large modifiers, the ISL holds true with any one point on that source. However, since there are indefinite sources, the spread of light from the other point also falls on to the area lit by the original point. Kind of like sharing light.

Block out all but any one point on a softbox, you will see the ISL return at those distances. This is because you are blocking the other light spilling on to the area lit by the point source.

Once you make the relative size of the large source smaller, the spread homogonizes to one source.

I cannot speak of a true focus fresnel lens and absolute parallell rays.
--
Film is a four letter word
 
antares103 said:
Perhaps i am off base here, but even with large modifiers, the ISL holds true with any one point on that source. However, since there are indefinite sources, the spread of light from the other point also falls on to the area lit by the original point. Kind of like sharing light.

Block out all but any one point on a softbox, you will see the ISL return at those distances. This is because you are blocking the other light spilling on to the area lit by the point source.

Once you make the relative size of the large source smaller, the spread homogonizes to one source.

I cannot speak of a true focus fresnel lens and absolute parallell rays.
Click to expand...
I understand your point and it’s interesting. I’m not professing to be an expert on ISL. Much of what I stated in my first post comes from my older books on the subject and what I’ve been taught. According to my reference material it seems (at least what I’ve read) is there is clear distinction made between a light source with divergent rays (like my example of a candle flame) and a light source which includes curved reflectors or broad sources of diffused light, parallel or converging rays.

As I’ve stated one has to be practical in terms of what a photographer might encounter in the studio. And for most purposes we’ve proven it works. After all we’re not going to the moon. :)
antares103 said:
--
Film is a four letter word
Click to expand...
--

I once had a perfectly exposed image of a white cow in a snow storm eating marshmallows.
 
This has all been gone through before, but here's my take on it. Continue to stamp feet or argue, but before you do, go out and satisfy the ISL with a pointsource. After that, you'll realise how wildly 'approximate' it is to real use.

The Inverse Square Law is a mathematical theory. There are all sorts of permutations which make this fail, the simplest being that the ISL works only for a pointsource and the law can only be applied approximately to any other modified source. 'Approximately' is a good word to bear in mind.

Here's the definition of the Inverse square law: Manual of photography: focal press:

The inverse square law applies strictly to point sources only. It is 'approximately' true for any source small in proportion to to it's distance from the subject. The law is generally applicable to lamps used in shallow reflectors, but not when deep reflectors are used. It is not applicable to the illumination provided by a spotlight'.

To satisfy my curiosity, I tried this out with a Lumedyne head @ 200ws with a coiled flash tube, I threw up a few lights and tried them:



The only use to satisfy the inverse square law (with this example) is the standard reflector, which I would put down to efficient reflector and tube design. None of the other uses satisfy the inverse square law at all.

The bare bulb should satisfy the Inverse Square Law yet it doesn't.

Not satisfied with this I built a custom environment to MAKE it work !

This time, I wrapped the non flash tube elements of the head in black velvet and masked much of the interior reflections. The head was pointed forward, and I obtained better results:



Environmental influences seem to impart a greater effect on the lighting than realised. Sometimes more than the modifiers themselves and definately more than I realised. In changing the environment the bare bulb benefitted considerably more than both the softboxes with only a small change in the smaller softbox being evident - primarily I think - down to masking the reflections.

I don't think I will achieve much better results than these in relation to proving the ISL, and in doing this I'm quite surprised at how closely modifiers do 'closely' follow the ISL. Whether this be in a more controlled environment as this test, or as the first test in a more regular environment.

And then there's environmental influences..

BTW: It's true that softboxes only approximately reflect the ISL. They only start to approximate the ISL at twice the softbox diameter. Closer and they fail completely.

Maybe it's easier to understand pictures.. Heres a couple of shots to show environmental variables.. should we expect the same results from the same single flash source ?

How soon should we note a change in results between the two scenarios, and

what do you think the difference in exposure level results are over an 8ft distance between the two examples?

These scenarios are a bit extreme, but you can't apply a Law with variables. Without these answers and creating an environment for the ISL to exist, then you can't prove the Inverse Square Law applies to anything. Needles to say, the results from these two different situations provide completely different results from the same softbox. Nothing to do with the softbox characteristics - entirely down to environment, which is why environment is so important.





Enjoy :)

.

--
Ian.

Samples of work: http://www.AccoladePhotography.co.uk
Weddings: http://www.AccoladeWeddings.com
Events: http://www.OfficialPhotographer.com

Theres only one sun. Why do I need more than one light to get a natural result?
 
Well said.

I, and I suspect most photographers, use the law as a rough guide to estimating how placing and moving lights will effect exposure. I start out with a plan for the quality of the light I want and choose a source, modifier and distance to produce that kind of light. I'll make some mental estimates of what power and camera setting combinations will work and give me the results I want. Then I'll grab a meter and measure the light.

I'm still fairly inexperienced compared to many folks here but even I have begun to develop a sense of what power I need at what distance with the lights and modifiers I use regularly.

The result is that I tend to use my actual experience more than any ISL based calculation. I know approximately how much to dial up the power if I move the softbox from 3' to 4'. I'm surprised at how often I guess correctly.
UKphotographers said:
The Inverse Square Law is a mathematical theory. There are all sorts of permutations which make this fail, the simplest being that the ISL works only for a pointsource and the law can only be applied approximately to any other modified source. 'Approximately' is a good word to bear in mind.
Click to expand...
--
-Dan Rode
http://rodephoto.com
 
DRode said:
The result is that I tend to use my actual experience more than any ISL based calculation. I know approximately how much to dial up the power if I move the softbox from 3' to 4'. I'm surprised at how often I guess correctly.
Click to expand...
Yes. But remember the environmental influence. Not everyone shoots in the same environment all of the time. I'd think the ISL would be the basis for experience to be derived from any lighting scenario.

 
UKphotographers

I really enjoyed reading your results....wow. I would have said the bare bulb worked in your first example but I understand your point. It only became "better" with a controlled environment.

Thanks :)

--

I once had a perfectly exposed image of a white cow in a snow storm eating marshmallows.
 
Jim Cassatt said:
The intensity of light falls off as the square of the distance.
Click to expand...
Simply put, "the square of the distance" is always twice the distance between the flash head and the subject.
The easiest distance to work with is ten feet (We all know our tens-right)?

So if the original distance between the two equals 10' and yeilds f/11, increasing the distance between the two to 15', the f/stop becomes f/13.

If the original distance is 5' and yields f/11, increasing the distance to 7.5' would yield f/13; simplicity in itself .
Jim Cassatt said:
The f-stop is also a square function such that the product of the f-stop and distance = a constant, called the guide number.
Click to expand...
Guide numbers are NOT a part of the original formula.
Jim Cassatt said:
--
Jim
http://www.pbase.com/jcassatt
Click to expand...
--
1200mm @ f/5.6 = imaging on steroids
 
photocellulite said:
Onetrack97 said:
photocellulite said:
Jim Cassatt said:
The intensity of light falls off as the square of the distance. The f-stop is also a square function such that the product of the f-stop and distance = a constant, called the guide number.

--
Jim
http://www.pbase.com/jcassatt
Click to expand...
Thanks. So wouldn't twice the distance equal 2 f-stops, not 1?
Click to expand...
Correct, twice the distance is equal to 2 fstops. Get a meter and try it.

Sound, twice the distance = 6 dB (think of 3 dB as one fstop).
--
Scott
Click to expand...
So that was my question. If you watched the video, they were doubling the distance, but accounting for only 1 stop difference in exposure.
Click to expand...
Not true: they accounted for both the original f/stop and the new f/stop they factored in.
 
photocellulite said:
ColourBlind said:
If it works for them, then great, but it didn't really do it for me.

Take a look at Zack Arias or David Hobby at Strobist for better info.

The inverse square law is basically - double the distance = quarter the light.

Because your light source is trying to illuminate a larger area.

What they seem to be talking about is the intensity of illumination being consistent over a distance from the camera.
Click to expand...
I understand the inverse-square law as it relates to point source light,
Click to expand...
"Point source light"? ??

I just didn't know what they were talking about, because their examples are wrong.

Agreed.
 
Razr said:
Simply put, "the square of the distance" is always twice the distance between the flash head and the subject.
The easiest distance to work with is ten feet (We all know our tens-right)?

So if the original distance between the two equals 10' and yeilds f/11, increasing the distance between the two to 15', the f/stop becomes f/13.

If the original distance is 5' and yields f/11, increasing the distance to 7.5' would yield f/13; simplicity in itself .
Click to expand...
I need one of those simple flash units you have then (unless I'm missing something).

As you increase your distance you're getting more output - that's just magic :)

--
Ian.

Samples of work: http://www.AccoladePhotography.co.uk
Weddings: http://www.AccoladeWeddings.com
Events: http://www.OfficialPhotographer.com

Theres only one sun. Why do I need more than one light to get a natural result?
 
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