The Inverse Square law and photography

[Garry Edwards]

You’ll find people quoting the Inverse Square Law all over the internet, in photography magazines and books, and if you believe what nearly all of these people say you’ll also believe that if you move a light twice as far from your subject you’ll end up with just a quarter of the light on your subject – but that isn’t right, and can be a reason why lighting doesn’t always work out as expected.

All of these people seem to speak with authority, so why am I saying that they’re wrong? Well, the ultimate authority is Sir Isaac Newton, so maybe we should look at what he said when he published his findings on 5 July 1687, long before we had any studio lighting....

The ISL actually states that a point source of radiated energy (light, heat, sound) quadruples the area that it covers every time it doubles its distance and that because of that only one quarter of the light that reaches any point will reach any point that is double the distance away. Here is the definition.

In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity. The divergence of a vector field which is the resultant of radial inverse-square law fields with respect to one or more sources is everywhere proportional to the strength of the local sources, and hence zero outside sources.

That can sound complicated so here’s my own explanation of what it means.

Now, a 'point source' is an unfocussed, tiny point of energy that does not and cannot actually exist in the practical world - but we can come close.
For example, a tiny torch bulb suspended on a piece of very thin wire, would come close if it was far enough away. It needs to be suspended because the light needs to be able to travel in all directions, otherwise it cannot quadruple its area of coverage each time it doubles its distance. Obviously, a softbox, a flashead reflector or any other kind of photographic light doesn't qualify, not only are they far too big but they also don't travel in all directions, so the chances of them quadrupling the area covered each time the distance is doubled is low, and probably close to nil.

The energy as described by Newton has to operate in free space. Free space is another term for a vacuum. Now, we don't operate in a vacuum do we? Actually that's only a fairly small point, all that a vacuum does is to produce a space free of airborne contamination, and a few bits of dust in the air doesn't make a lot of difference, but it’s still a factor even if it’s only a small one.

The source of energy must be free from outside sources. That means that there must be no other forms of the same type of energy (light) present to affect the result, and there must be no reflection of light from things like walls and ceilings. What this means is that unless your point source of light is the only source of light, and unless it also happens to be stuck on the top of a high mountain at night, with no moon or stars visible, the ISL doesn't work, or at least cannot follow the formulae.

Now, I had to study physics before I could do my photography degree, and the one thing that I learned was to challenge and test everything, and to take no notice of anything I read in photography magazines (we didn't have the internet then but it certainly applies to that too so I tested the theory for myself. I found it so interesting that I made a video about it.

Using a softbox in my studio (which is much larger than most and which doesn't have any nearby walls to reflect light, and which of course has a black ceiling) I got this:
Benchmark test, 0.5 metre from softbox = f/22
1 metres from softbox = f/16 d1 (not the 'expected' f/8
2 metres from softbox = f/8 d4 (not the 'expected' f/5.6
4 metres from softbox = f/4 d8, not the 'expected' f/2.8

A softbox is a bit of a special case, because the light source is so large and because it comes from so many different directions at once, but I used a softbox because they are very popular tools for studio photographers.
An identical test with a reflector instead of a softbox produced very similar results, as it would.

Now, that's an error that ranges up to 180% (or up to 1.8 stops) from what people who don't understand the inverse square law thinks they should get - personally I would call that a significant error, well worth knowing about..

Those results are pretty much what I expected, based on my knowledge of lighting and of the inverse square law.

Lighting tools that use optical or physical means to collimate light will not follow the inverse-square relationship at all. These tools include optical spots (Focusing spots, Fresnel spots) and sources whose beam has been modified by a honeycomb grid, and of course laser beams.

The inverse-square fall-off (even though, as I’ve explained, doesn’t follow the formulae) also explains why power requirements can vary widely. A portrait photographer doing headshots can get by with a couple of hundred watt-seconds of flash energy, but a fashion photographer may need several thousand to light his larger and deeper set. A fashion photographer working in a large studio might want the fall off of light to be slight, so that the background and set gets almost as much light as the front subject, so has to place the lighting a long way away.

I’m sure that there will be people on here who disagree with what I’ve said – so let’s have a discussion

 

[BigJohn]

A very interesting read Garry . I can just about get my head around it . It just appears that in practice there are too many variables to account for to use the law to it's word .

 

[mike weeks]

One problem with this test is that newton was talking about a constant light source and not a pulsed light source like a flashgun which does not produce an instantaneous output as Gary can possibly explain far better - would there be a difference using hot or cold constant lighting? I dont know but I know a man that is capable of testing it.

Mike

 

[Stoptime]

Your figures seem to demonstrate the inverse square law quite well.

If you ignore the 0.5m measurement (it is a softbox and at that distance nothing like a "point source".

At 1m the reading is f16 - call that the reference
At 2m, twice the distance, the reading is f8 (2 stops down), a quarter of the intensity.
At 4m, four times the distance, the reading is f4 (4 stops down), a sixteenth of the intensity)

 

[Garry Edwards]

One problem with this test is that newton was talking about a constant light source and not a pulsed light source like a flashgun which does not produce an instantaneous output as Gary can possibly explain far better - would there be a difference using hot or cold constant lighting? I dont know but I know a man that is capable of testing it.

Mike

Actually he was talking about any form of radiated energy - heat, sound or light - and it makes absolutely no difference whether the source is a pulse of light (flash) or continuous.

Your figures seem to demonstrate the inverse square law quite well.

If you ignore the 0.5m measurement (it is a softbox and at that distance nothing like a "point source".

At 1m the reading is f16 - call that the reference
At 2m, twice the distance, the reading is f8 (2 stops down), a quarter of the intensity.
At 4m, four times the distance, the reading is f4 (4 stops down), a sixteenth of the intensity)

No, my figures don't reinforce the ISL at all, you've missed out the all-important 'd'. I apologise for not explaining 'd' which is the standard abbreviation used by photographers for 'decimal'. A flash meter typically measures in whole stops plus 'd' - for example f/5.6 d 5 means f/5.6 decimal 5, which is .5 of a stop more than f/5.6, in other words half a stop brighter than f/5.6.
For convenience, forget about the f/16 decimal 1 in what you want to call the reference at 1 meter and call it f/16

1 metres from softbox = f/16 d1

Therefore, at 2m the ISL says that the reading should be f/8, in fact it was f/8 d4, which is 40% of a stop out.

And at 4m the ISL says that the reading should be f/4 at your calculation, in fact it was f/4 d8, which is 80% of a stop out

As with everything you read, don't take anything at face value, test it for yourself. If your testing conditions are exactly the same as mine you can expect to get exactly the same result. If the conditions are different you'll get a different result, and it the shooting conditions are a small room with close, white surfaces then the light bounce will produce figures that are even further from the 'expected' figures than my test shows.

 

[gman]

Very interesting stuff and for me it has made me think about why this wasn't so obvious in the first place, specifically this part:

the light needs to be able to travel in all directions

I don't know enough about physics or tried to look it up, but can air pressure, air temperature or humidity effect how light can travel?

 

[Garry Edwards]

Very interesting stuff and for me it has made me think about why this wasn't so obvious in the first place, specifically this part:

Quote:
Originally Posted by Garry Edwards
the light needs to be able to travel in all directions

I don't know enough about physics or tried to look it up, but can air pressure, air temperature or humidity effect how light can travel?

Well, you've identified the crux of it, the main reason why the inverse square law doesn't apply in the way that people assume it to - if the direction of the light is controlled in any way then it can't disperse freely and so can't quadruple the area covered each time it doubles its distance, leaving only a quarter of the power at any given point.

I can't answer your question about the effect of air pressure, air temperature or humidity because I only did physics up to 'A' but I'm sure there will be others who may be able to help on that. My guess is that the answer will be 'Yes' simply because, all other conditions being present, the ISL only truly works in free space (a true vacuum)

 

[arad85]

I don't know enough about physics or tried to look it up, but can air pressure, air temperature or humidity effect how light can travel?

Yes, think of how fog works (it's just air at a different temp/humidity level). Having said that, for all practical distances and especially indoors, I think the effect would be negligible.

 

[Triggaaar]

Good stuff Garry. I think the point to take from your notes are that we should do our own test and not rely on the rule as a given, because there can be external factors (eg reflective walls) that change the results.

I disagree with this basic point:

Obviously, a softbox, a flashead reflector or any other kind of photographic light doesn't qualify, not only are they far too big but they also don't travel in all directions, so the chances of them quadrupling the area covered each time the distance is doubled is low, and probably close to nil.

A light doesn't have to travel 360 degrees for it to obey Newton's law, it would work for the shapes that our lights make. The size of the source does reduce the effect so as you say, for a softbox the area lit does not quadruple as distance doubles.

 

[Garry Edwards]

Good stuff Garry. I think the point to take from your notes are that we should do our own test and not rely on the rule as a given, because there can be external factors (eg reflective walls) that change the results.

Originally Posted by Garry Edwards
Obviously, a softbox, a flashead reflector or any other kind of photographic light doesn't qualify, not only are they far too big but they also don't travel in all directions, so the chances of them quadrupling the area covered each time the distance is doubled is low, and probably close to nil

I disagree with this basic point:A light doesn't have to travel 360 degrees for it to obey Newton's law, it would work for the shapes that our lights make. The size of the source does reduce the effect so as you say, for a softbox the area lit does not quadruple as distance doubles.

Mike,
Leaving aside the problems caused by reflected light, which is a given, I'm right unless a particular light/modifier combination behaves exactly as if it were a point source of light, i.e. unless the light quadruples in area every time it doubles its distance.

Testing it for yourself will tell you whether your particular light spreads at that angle or not.

 

[Michael Sewell]

I used to use/abuse the ISL a long time ago, and eventually stopped using it when I figured out that moving a light source one third of the distance towards the subject increased the exposure by about one full stop. And conversely, moving the light source half the distance again from the subject decreases the exposure by about one full stop.

It just made my life so much easier )

 

[Triggaaar]

I'm right unless a particular light/modifier combination behaves exactly as if it were a point source of light, i.e. unless the light quadruples in area every time it doubles its distance.

My point is that the light does not have to travel in every direction for it to obey the law. From your original post:
"For example, a tiny torch bulb suspended on a piece of very thin wire, would come close if it was far enough away. It needs to be suspended because the light needs to be able to travel in all directions, otherwise it cannot quadruple its area of coverage each time it doubles its distance."
If you took that same tiny torch bulb and put a large 100% absorbing black sheet next to it, the rule still applies. It will still quadruple its area of coverage each time it doubles its distance. Instead of one black sheet you could have two, effectively placing the bulb in a corner, and the rule will still apply. Using these 100% black sheets you could make a cone shape light modifier, and the rule will still apply.

 

[Garry Edwards]

My point is that the light does not have to travel in every direction for it to obey the law. From your original post:
"For example, a tiny torch bulb suspended on a piece of very thin wire, would come close if it was far enough away. It needs to be suspended because the light needs to be able to travel in all directions, otherwise it cannot quadruple its area of coverage each time it doubles its distance."
If you took that same tiny torch bulb and put a large 100% absorbing black sheet next to it, the rule still applies. It will still quadruple its area of coverage each time it doubles its distance. Instead of one black sheet you could have two, effectively placing the bulb in a corner, and the rule will still apply. Using these 100% black sheets you could make a cone shape light modifier, and the rule will still apply.

You've made a fair point there but...
Regardless of whether or not the light is free to travel in all directions, lights used in photography are almost always (a possible exception being a bare bulb flash) directed in just one direction, and if the light is controlled in a way that prevents it from quadrupling its area each time the distance is doubled, the ISL cannot apply to it.

Same with any other form of radiated energy, for example sound transmitted through a megaphone doesn't obey the ISL either, nor does heat reflected to throw at a narrow angle.

Newton's theory is of course absolutely right, but the point I'm trying to make is that it ONLY applies if all the conditions are met, and they aren't met in the real world.

 

[HoppyUK]

Garry, I'm not sure what the point of your post is. It appears to be that the inverse square law should be disregarded because it's miles out when applied to photography.

I think this is not only unhelpful, but also untrue - as your own figures demonstrate.

Of course, we don't use true point light sources or operate in vacuums, but as a rule of thumb, the ISL is a very helpful practical guide and you ignore it at your peril. Your figures from 1-2m show a drop of 1.7 stops, from 2-4m a further 1.6 stops. That's not two stops as the theory says, but it's not far off. And you are using a large softbox!

Do the same thing with a hot-shoe gun, which is pretty close to a point light source as far as we're concerned. Fire it at a plain wall, and if you double the distance the pool of light is exactly double the diameter and so four times the area - a drop of two stops.

Anyway, I just tried it out on the patio. It's dark, and there is as close to zero light reflected back from anywhere as possible. From 1-2m I get exactly 2.0 stops reduction, and at 4m another 2 stops exactly. As it must be if the light is covering four times the area.

If I do the same test indoors though, in a normal domestic room, the numbers change a bit, due to the influence of reflected light from the ceiling walls. In that situation, the drop from the same hot-shoe gun is 1.9 stops from 1-2m, and a further 1.7 stops from 2-4m. This still seems to be as close to the ISL as makes no difference (the figures get even closer to parity if you zoom the flash head to tele, reducing the influence of reflections).

Inverse square law is alive and well down here

Edit: the point I would make is, most forms of studio light fall off very rapidly with distance - usually more than you might expect, and the closer you are, the more critical small changes of distance become. If you have a light 1m from the subject, and a white backgound 1m behind them (not an untypical scenario) then newcomers are always confused as to why the background comes out grey (because it would be white if they had the same subject and background outside in the sun). It might not follow the ISL exactly, it might not be as much as two stops down, but as a rule of thumb, it's going to be somewhere around that.

 

[Splog]

<snip> but...
Regardless of whether or not the light is free to travel in all directions, lights used in photography are almost always (a possible exception being a bare bulb flash) directed in just one direction, and if the light is controlled in a way that prevents it from quadrupling its area each time the distance is doubled, the ISL cannot apply to it.

</snip>

Hi Gary

Not sure about this.... but! ... if? as you say, the light is focussed in one direction then how does it not still follow the ISL and just how do you measure the light source? Surely if the light is being directed then it is no longer acting in free space?...... Perhaps I've missed something here? but even if I have then surely the light still follows the ISL..... The only exception I can think of would be a laser light source! ...... certainly any conventional simple torch would obey the theory!

 

[Triggaaar]

What I would take from your point Garry is that the size of the light source can make a big difference (for example when using a large softbox at close distances) and reflections can also make a noteable difference too.

 

[Garry Edwards]

Garry, I'm not sure what the point of your post is. It appears to be that the inverse square law should be disregarded because it's miles out when applied to photography.

I think this is not only unhelpful, but also untrue - as your own figures demonstrate.

Of course, we don't use true point light sources or operate in vacuums, but as a rule of thumb, the ISL is a very helpful practical guide and you ignore it at your peril. Your figures from 1-2m show a drop of 1.7 stops, from 2-4m a further 1.6 stops. That's not two stops as the theory says, but it's not far off. And you are using a large softbox!

Do the same thing with a hot-shoe gun, which is pretty close to a point light source as far as we're concerned. Fire it at a plain wall, and if you double the distance the pool of light is exactly double the diameter and so four times the area - a drop of two stops.

Anyway, I just tried it out on the patio. It's dark, and there is as close to zero light reflected back from anywhere as possible. From 1-2m I get exactly 2.0 stops reduction, and at 4m another 2 stops exactly. As it must be if the light is covering four times the area.

If I do the same test indoors though, in a normal domestic room, the numbers change a bit, due to the influence of reflected light from the ceiling walls. In that situation, the drop from the same hot-shoe gun is 1.9 stops from 1-2m, and a further 1.7 stops from 2-4m. This still seems to be as close to the ISL as makes no difference (the figures get even closer to parity if you zoom the flash head to tele, reducing the influence of reflections).

Inverse square law is alive and well down here

Edit: the point I would make is, most forms of studio light fall off very rapidly with distance - usually more than you might expect, and the closer you are, the more critical small changes of distance become. If you have a light 1m from the subject, and a white backgound 1m behind them (not an untypical scenario) then newcomers are always confused as to why the background comes out grey (because it would be white if they had the same subject and background outside in the sun). It might not follow the ISL exactly, it might not be as much as two stops down, but as a rule of thumb, it's going to be somewhere around that.

Richard,
Thanks for your contribution.

Yes, there will be times when the output from a hotshoe flash will approximate the ISL, but often it doesn't. You know, I found out that the ISL doesn't work with photography lights in my very first job as a trainee photographer. We used flashbulbs in those days and the boxes of bulbs had a little scale on them, showing what the exposure should be at any given distance - based of course on the ISL. I found out that it was sometimes up to 2 stops out but, at that time, didn't have the education to work out why. So I asked my boss, who happened to be W.D. Emmanuel, one of the greatest photographic technicians of his time, and he explained it all to me. But he did more than that, he gave me a big box of flashbulbs and a few rolls of film so that I could test it for myself, rather than take his word for it. My actual employer was Wallace Heaton's, not the most generous of firms, but Emmanuel himself was a very generous man and very helpful to people who genuinely wanted to learn.

And you are using a large softbox!

Yes I am - is there something wrong with using a large softbox? Surely it's the tool of choice for most people who use studio lighting and you yourself are always advising people to get the biggest softbox they can

But I'm not relying on just the large softbox to illustrate my point. Tests done in exactly the same testing environment at the same time with a reflector showed the following results:
At 0.5 m f/22 (benchmark)
At 1 m f/11 d6, an error of .4 stops
At 2 m f/5.6
At 4 m f/4 d3, an error of 1.3 stops

Depending on both the light source and the shooting conditions, sometimes the ISL can be a useful guide, sometimes it can be way off.

 

[Garry Edwards]

Hi Gary

Not sure about this.... but! ... if? as you say, the light is focussed in one direction then how does it not still follow the ISL and just how do you measure the light source? Surely if the light is being directed then it is no longer acting in free space?...... Perhaps I've missed something here? but even if I have then surely the light still follows the ISL..... The only exception I can think of would be a laser light source! ...... certainly any conventional simple torch would obey the theory!

Steve,
Yes, reflections aside, a simple torch will follow the ISL pretty well, but they aren't exactly common lighting tools in the studio.
As I said in my original post:

Lighting tools that use optical or physical means to collimate light will not follow the inverse-square relationship at all. These tools include optical spots (Focusing spots, Fresnel spots) and sources whose beam has been modified by a honeycomb grid, and of course laser beams.

These lighting tools retain most of their energy, the tools prevent the light from spreading out, and if it can't spread out as assumed by the ISL then the fall off of light is nowhere near as great.

The whole point of this thread (other than the fact that I've got time on my hands following my op, can't do anything physical, can't go shooting and can't even drive) is that I think it's important to understand that, like all immutable laws of physics, the ISL only works when the qualifying conditions are met, and they are not met with photographic lighting, so the 'rule' only becomes no more than a rough guide. That doesn't make it useless, but it does mean that it needs to be tested, and it will usually fail the test.

 

[Triggaaar]

Tests done in exactly the same testing environment at the same time with a reflector showed the following results:
At 0.5 m f/22 (benchmark)
At 1 m f/11 d6, an error of .4 stops
At 2 m f/5.6
At 4 m f/4 d3, an error of 1.3 stops

That's interesting, from 1m to 2m you've got more than 2 stops drop, and from 2m to 4m less than 1 stop. I expect there's some measurement errors in there too.

 

[Garry Edwards]

That's interesting, from 1m to 2m you've got more than 2 stops drop, and from 2m to 4m less than 1 stop. I expect there's some measurement errors in there too.

No, there was no measurement error. I used my Minolta flash meter, 5 samples taken at each distance.

 

[arad85]

No, there was no measurement error. I used my Minolta flash meter, 5 samples taken at each distance.

What would cause the highly non-linear dropoff then Garry?

 

[irelanst]

I would assume that the majority of the error is due to the fact that the softbox face is very large (in comparison to the light meter sensor).

Assuming that the light meter is placed centrally with the face of the softbox, the light from the centre travels a much shorter distance to the sensor than the light from the edges. Also the light emitted from the edges of the softbox which is incident on the light meter sensor will have quite an acute incident angle, which will reduce its apparent intensity.

As the softbox is moved farther away then this differential becomes less significant and the softbox will be a closer approximation to the ISL, as it more closely approximates a point source. If you could integrate the total light intensity of the softbox onto a background for instance then I would imagine that it would be a good approximation to the ISL regardless of distance.

All IMHO, I have absolutely no evidence to back any of this up and no experience of studio lighting!

Steve

 

[Garry Edwards]

Steve,
You may have no evidence and no experience of studio lighting, but you're pretty well right, although I'm not sure that the angle of incidence of the light from the edges of the softbox to the sensor (which is a 180 degree dome) is relevant! But it would have been relevant if I had used a flat receptor. Flat receptors are typically used for measuring flat (2 dimensional) subjects but most people use dome receptors, so I did too.

As a very rough guide, a softbox needs to be at least twice its longest dimension from the subject (for example: a medium softbox, 4' x 3', measures 5' corner to corner so needs to be at least 10' from the subject) for the size of the softbox to avoid skewing the results badly.

Trouble is, softboxes are typically used quite close to the subject, or a least they are if soft, wraparound lighting is required. In 'tabletop' still life photography, where the subject is highly reflective and diffused specular reflections are needed, they are often only a few inches away.

I'm getting a few negative comments on this thread (I'm sure that they're not intended to be negative) pointing out that I've used a large softbox as a test source - although I got similar results with an ordinary reflector - but the fact of the matter is that most people who use studio lighting do in fact use large softboxes, so I think my test source is a good choice.

 

[irelanst]

Not intended as a negative from me Gary, I was trying to apply some logical explanation as to why the softbox (and most other soft light modifiers) will not appear to obey the ISL over the distances they are used in photography.

As I said, I know very little about studio lights, but do know quite a bit about radiation (of heat mainly, but the same principles apply to light) because I do computational thermodynamics for a living (I know not very rock and roll is it).

Thanks for the explanation on light meters, that makes a lot of sense, I don’t know anything about those either! I think that the edges of the softbox will still seem less bright than the centre though due to the radiant angle from the sofbox surface (assuming the softbox has a flat diffuser which obeys Lambert cosine law)

 

[Garry Edwards]

You're right about the effects of cosine law too; and about other forms of radiated energy - it's good to come across someone who understands physics

Basically a flash meter is just a simple measuring device with a few resistors and a hefty price tag,

this is the one I use, you can see the dome (2).

 

[HoppyUK]

<snip>
a flashead reflector or any other kind of photographic light doesn't qualify, not only are they far too big but they also don't travel in all directions, so the chances of them quadrupling the area covered each time the distance is doubled is low, and probably close to nil.

<snip>

If you feel you are getting negative feedback Garry, then it's probably because of that sentence above And your general stance that comes across as dismissing the ISL as having any no relevance.

I would say just the opposite, and as a basic principle the ISL is certainly the best guide we've got. It applies strictly to a point light source in a controlled environment, and a softbox in a domestic studio is quite a long way from that, but still if you move the light back to double the distance then you should expect a very substantial fall-off. Maybe not exactly two stops at double the distance, but probably 1.6-ish which is not far off (in line with your tests). As a working rule of thumb, it is a vital guide and the theory that underpins it is the ISL.

I don't know about your box of flashbulbs Garry, but when we all used guide number tables to work out the exposure from our flash guns, they always followed the ISL exactly. And they still do.

Simple test. Fire a hot-shoe gun at a plain wall and adjust it for correct exposure at a highish f/number. Now move it back to exactly twice the distance and take a number of shots at a range of lower apertures in 1/3rd stop increments. The one that is two stops lower will be closest to matching the first exposure. It cannot be otherwise.

The difference comes when you swap the hot-shoe gun for a much bigger softbox or brolly, which is obviously a million miles from a point light source. Do the same test with that and the fall off will be less than two stops, in the region of 1.5 to 1.8 because of the larger light area and also reflected spill from the ceiling/walls, but as a practical guide that's not far off when you're setting up the lights. If you take that same softbox outside (no ceiling/walls) and do the same test at greater distance, like maybe 3m and 6m which makes the softbox relatively much smaller, you will find find the difference is very close indeed to exactly two stops which proves that softboxes are absolutely not immune to the ISL.

If you were to change your post and say that softboxes used at close range don't follow the ISL exactly but are close to it, then I wouldn't have any problem with that at all. Or put another way, don't use guide numbers to work out the exposure with a softbox (like the guide numbers Lencarta and every other manufacturer uses as a measure of light output). But as it stands, I think your post is very misleading. Interesting, but misleading

 

[Hodders]

The theory behind radio transmitters and studio flash is identical.

A radio transmitter is often designed to have a beam shape that allows transmission in one direction only (think standard reflector on a flash head). In this case the beam pattern can be used to work out the EIRP or Equivalent Isotropically Radiated Power - or in English - how powerful would the equivalent point source radiating uniformly in all directions in an infinitely large dark vacuum have to be to have the same observed power at the single point of the observation.

Consider a light source with a reflector (acting as a point source - impossible but lets run with it), moving backwards and forwards along a line pointing back to the light source will then follow the ISL - it has to - as there is no way of the observer knowing if the transmitter (a point source remember) is radiating in all directions or just towards the observer. All you can tell given your distance to the light is its EIRP, you can tell nothing of its beam shape without moving from side to side.

Once the light ceases to be a point source all this disappears and the maths gets harder as you are effectively integrating the received light from an infinite number of point sources at a given point. At this point most normal heads start to hurt !

 

[Garry Edwards]

Ben, what you say about radio transmissions makes sense too. I believe that modern technology has pretty well cured all the problems, but back in the early days signals didn't reach very far and were very much affected by air pollution caused by weather. I remember that back in 1909 when the Republic sent the first ever successful distress signal it only just reached 60 miles, back on those days radio operators had to relay messages onwards by manually re-sending them - which is why the distress signal "CQD" could be mistaken for CQ (all ships all stations) - relay as there was very little difference between the morse for CQD (distress) and the morse for CQ relay (CQDE) - just a single dot for the e - Hence the change to SOS.

Back on topic, I fully accept that there are times when the ISL is 'near enough' for photography but there are many times when it just isn't, and I get a bit wound up when people misquote it, assuming that it works when it really doesn't.

I watched this video, produced by so-called pros, where they talk about the ISL (at about 2 mins 40) and say that it applies to the Fresnel Spots they're using - which it patently doesn't, as Fresnel Spots produce a collimated light. What I am not saying is that theory never translates into practice, what I am saying is that it often doesn't and people shouldn't assume that the ISL will always apply, because it certainly doesn't, much of the time. Everyone should do their own testing, with their own light shaping tools in their own environment, and ignore most of what they see and read.

 

[Hodders]

Garry, sure things like rain fade, cloud cover all have a impact on electromagnetic transmission and propagation. Luckily we don't need to worry too much about those ina typical studio environment.

Given that a fresnel spot has a much smaller transmitting area than a 150cm softbox I would maintain that the ISL will apply more accurately here than with many other modifiers....

Some very quick readings using my snoot (minimize spill etc) were:

1m f32 (set as accurately as I could)
2m f16 (1/4 the light so spot on !)
4m f8 (1/4 the light so again about right)

Got to pick my son up from nursery now, so no time to test the softbox.

 

[HoppyUK]

Ben, what you say about radio transmissions makes sense too. I believe that modern technology has pretty well cured all the problems, but back in the early days signals didn't reach very far and were very much affected by air pollution caused by weather. I remember that back in 1909 when the Republic sent the first ever successful distress signal it only just reached 60 miles, back on those days radio operators had to relay messages onwards by manually re-sending them - which is why the distress signal "CQD" could be mistaken for CQ (all ships all stations) - relay as there was very little difference between the morse for CQD (distress) and the morse for CQ relay (CQDE) - just a single dot for the e - Hence the change to SOS.

Back on topic, I fully accept that there are times when the ISL is 'near enough' for photography but there are many times when it just isn't, and I get a bit wound up when people misquote it, assuming that it works when it really doesn't.

I watched this video, produced by so-called pros, where they talk about the ISL (at about 2 mins 40) and say that it applies to the Fresnel Spots they're using - which it patently doesn't, as Fresnel Spots produce a collimated light. What I am not saying is that theory never translates into practice, what I am saying is that it often doesn't and people shouldn't assume that the ISL will always apply, because it certainly doesn't, much of the time. Everyone should do their own testing, with their own light shaping tools in their own environment, and ignore most of what they see and read.

"What I am not saying is that theory never translates into practice..." That's exactly what you did say Garry, more than once, and it's not true. As a five minute test with a flash gun demonstates (and they have Fresnel lenses in them too). It's not absolutely true with a softbox at close distance, but your own tests show that it's not very far off and as a basic guiding principle it's a damn good starting point.

It's a fundamental principle of physics and one of the first things anybody using any form of artificial light needs to understand - flash guns, studio lights, video lights, whatever. Then if you find that the particular light source you're using doesn't follow the law exactly, then modify it, but it will never be far out.

Furthermore, you've misunderstood what the guy on the linked video is saying (he's the one that also does the Pocket Wizard demos too BTW). He's not talking about the ISL in terms of exposure and is actually referring to a side effect of it. He says that because of the ISL "when we bring a light further from the background it spreads out and becomes more even" which in that particular case, it does.

Basically he's saying that if the light has a bit of a hot-spot then moving it back will make the pool bigger and therefore the illumination more even over more of the subject. I think we've all used that technique, not the ISL in the sense of exposure exactly, but a practical side effect of it as the pool becomes larger.

 

[arad85]

This got me thinking and led to a gfoogle search (which is what normally happens in these cases). It came up with: http://www.portraitlighting.net/inversesquare_law.htm

Makes some interesting reading, and makes the point that with things like Fresnel lenses, what you are doing is emulating a beam from a much brighter point source much further away. I.e. doubling the distance means doubling it from your effective point source....

 

[Garry Edwards]

"What I am not saying is that theory never translates into practice..." That's exactly what you did say Garry, more than once, and it's not true.

And where did I say that?
I know I've only got one working eye at the moment but I can't seem to find it

Edit: Can't find where I said that the theory never translates into practice, I can find the eye - it's under the patch

 

[HoppyUK]

And where did I say that?
I know I've only got one working eye at the moment but I can't seem to find it

Edit: Can't find where I said that the theory never translates into practice, I can find the eye - it's under the patch

How else are we supposed to interpret these quotes?

<snip>
if you believe what nearly all of these people say you’ll also believe that if you move a light twice as far from your subject you’ll end up with just a quarter of the light on your subject – but that isn’t right, and can be a reason why lighting doesn’t always work out as expected.
<snip>
Obviously, a softbox, a flashead reflector or any other kind of photographic light doesn't qualify, not only are they far too big but they also don't travel in all directions, so the chances of them quadrupling the area covered each time the distance is doubled is low, and probably close to nil.
<snip>
What this means is that unless your point source of light is the only source of light, and unless it also happens to be stuck on the top of a high mountain at night, with no moon or stars visible, the ISL doesn't work, or at least cannot follow the formulae.

This got me thinking and led to a gfoogle search (which is what normally happens in these cases). It came up with: http://www.portraitlighting.net/inversesquare_law.htm

Makes some interesting reading, and makes the point that with things like Fresnel lenses, what you are doing is emulating a beam from a much brighter point source much further away. I.e. doubling the distance means doubling it from your effective point source....

Good link

In practical terms, this is the crucial bit:
"You can use the inverse-square law to predict the rate of illumination fall-off for bare-bulb sources, speedlights, and studio strobes. Umbrellas and softboxes will follow the law quite closely for distances greater than twice their diameter. So, what are the exceptions?

"Sources that use optical or physical means to collimate light will not follow the inverse-square relationship, at least when based on their physical location. Such devices include, optical spots (elliptical, Fresnel) and sources whose beam has been modified by a grid. When working very close to large, diffuse sources, such as softboxes* and scrims, the fall-off rate will be somewhat less than predicted by the inverse-square law."

*In practical terms, as a working rule of thumb, the fall-off rate is about 1.5 stops instead of 2.0 stops at close range with a softbox. So that's a bit less than the ISL, but still a very rapid reduction. At the same time, when you're working close even small changes of distance make a big difference, like move the light one foot and you'll need to adjust the exposure.

 

[Matt]

if the inverse square law is applied in my business, it has caveats attached.

[FONT=&quot]point source basic calculation (spherical source) S = 4[/FONT]p[FONT=&quot]r2 [/FONT]

this is 1 source with no boundaries. So in acoustics the basic sound power would be 1/4 the intensity at twice the distance from the source, however if you introduce reflections from surfaces then you change the equation, does this apply to light too? You'd have to have light absorbing surfaces on all surfaces for there to be no diffuse light interfering with the measured light?

 

[Matt]

to add to this, if a sound source is measured, its intensity measured and inverse square law applied, then you would have a drop off of 6dB per doubling of distance. In reality however the ISL only actually applies to a very narrow band (called room radius i think) but the area before and after this are both interfered with by the room, the near field and the far field. The near field does not decrease as rapidly as the sound source is actually more of a Wall Source(and so changed Q) than point source, while the far field is made up of late arriving reflections, which make the levels tail off more than expected.

 

[Garry Edwards]

if the inverse square law is applied in my business, it has caveats attached.

[FONT=&quot]point source basic calculation (spherical source) S = 4[/FONT]p[FONT=&quot]r2 [/FONT]

this is 1 source with no boundaries. So in acoustics the basic sound power would be 1/4 the intensity at twice the distance from the source, however if you introduce reflections from surfaces then you change the equation, does this apply to light too? You'd have to have light absorbing surfaces on all surfaces for there to be no diffuse light interfering with the measured light?

Yes it does. Newton's theory applies equally to all point sources of radiated energy.

Problem is, in the real world, even large pro studios are a bit short of light absorbing surfaces. And in small home studios, light absorbing surfaces are very thin on the ground.

 

[Somelier]

however if you introduce reflections from surfaces then you change the equation, does this apply to light too? You'd have to have light absorbing surfaces on all surfaces for there to be no diffuse light interfering with the measured light?

Most certainly. The inverse square law only works precisely where there is a point source of light and no other light falling on the subject. A flashgun is not a point source of light, but can be considered so if you take into account the angle that the light is leaving the flashgun and work that back to a virtual point.

I work with flash a lot outdoors and before the days of TTL flash metering, I used to use a rotary calculator to calculate the distance required from the flash to the subject. The first thing that was necessary was to divide the guide number of the flash by 4. This was to compensate for the lack of reflective surfaces that would normally be in a room - which was the normal environment that the guide number was calculated for by the manufacturer.

Frankly, you can argue all day over the relevance of the IVL, but as long as there is some understanding of the basics, then that's enough to make sense of why the aperture changes with the flash to subject distance. It's far easier to use TTL metering or a flash meter than to try and calculate the IVL.

I can't help thinking that the OP is just trying to blind us with science to show us how clever he is!

 

[Garry Edwards]

I can't help thinking that the OP is just trying to blind us with science to show us how clever he is!

Then you're not thinking straight. What the OP is trying to do is to get people to think, and to test these things for themselves, not just to believe everything they read.

That isn't trying to prove that I'm clever, that's just encouraging other people to be clever. The clever one here was Newton, with his IQ of 190. All that I've actually tried to do is to get people to read what he actually said, not to believe that lights that are very different from point sources, in environments very different from the theoretical environments set out in the ISL, will always behave in the same way as point sources of light in free space.

 

[Matt]

is there the equivilant of near and far field in light? those are the things that are interfering with the measurements..

 

[Garry Edwards]

to add to this, if a sound source is measured, its intensity measured and inverse square law applied, then you would have a drop off of 6dB per doubling of distance. In reality however the ISL only actually applies to a very narrow band (called room radius i think) but the area before and after this are both interfered with by the room, the near field and the far field. The near field does not decrease as rapidly as the sound source is actually more of a Wall Source(and so changed Q) than point source, while the far field is made up of late arriving reflections, which make the levels tail off more than expected.

I take it this is 6db on the A scale? I think that that would follow the ISL.

is there the equivalent of near and far field in light? those are the things that are interfering with the measurements..

Too technical for me, I know that those particular terms have relevance in specialist lighting and scientific applications, but they're outside of my own knowledge. But, regardless of terminology, it seems that the interference to the theoretical ISL figures in acoustics is similar to that of light - unwanted reflections.

Of course, in light, reflections aren't always unwanted - it's just that they interfere (sometimes dramatically) with the control of light