The Inverse Square Law and Why It Is So Important for Lighting

The inverse square law is by far one of the most fundamental and important concepts that every photographer working with artificial light should understand. If that is something you struggle with a bit or you have not heard of it before, this fantastic video will get you up and running in no time at all.

Coming to you from Matt Granger, this great video tutorial will show you how the inverse square law works. The issue is that humans are generally pretty bad at estimating things that do not behave linearly, and if you are not aware of how light deviates from linear (and thus intuitive) behavior, it can be a bit confusing when you are learning how to use strobes. In essence, the inverse square law says that light intensity decreases as the square of distance; in other words, if you double the distance, the intensity drops to a quarter strength. If you triple the distance, it drops to a ninth the original strength. Once you get the hang of it, it is pretty easy to work with and will help you better light your subjects. Check out the video above for the full rundown from Granger. 

If you would like to continue learning about lighting, be sure to check out "Illuminating The Face: Lighting for Headshots and Portraits With Peter Hurley!"

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Jacques Cornell's picture

Inverse square law applies to point sources in empty space. Actual lighting mods behave differently, the most obvious being parabolic reflectors that throw a tight cone of light, such that light intensity decreases quite gradually with distance. Also, walls, floors and ceilings that are not black reflect back to the subject light that is otherwise assumed by the inverse square law to have been lost.
I use a large silver parabolic umbrella for small group portraits in part because exposure on a subject 6 feet from the source is only about 0.2 stops less than on a subject 3 feet from the source.

Bert Nase's picture

You are talking about absorption and reflection. The inverse square law is about the travelling of light. That's physics. When the light is reflected by a wall, do you think it's travelling slower than? You can look at the wall as a new light source for which the physics are the same. Move you light that you're throwing against the wall away and you'll see that less light hit's the wall and of course less light will be reflected...

Jacques Cornell's picture

I'm talking about the theoretical conditions of the inverse square law vs. real-world shooting conditions. The law describes a point source radiating in all directions equally in empty space.
Even a bare-bulb flash in a studio behaves nothing like this unless most of the surfaces are black.
I bring it up because it's important for working photographers to understand the real-world relationship between distance and light intensity in actual working conditions with actual light sources and mods.
I also mentioned parabolics because many photogs aren't aware that they render the ISL almost entirely irrelevant in studio conditions
In case any of y'all are wondering, I've been working professionally with every kind of studio and location lighting equipment most of you have ever heard of, and some you haven't, for 20 years.
If you still don't believe me, get a large silver PLM (they're cheap) and try it yourself. Best mod money I ever spent.

Tammie Lam's picture

Jacques Cornell Focused true parabolics (Broncolor Para, Briese, Parabolix aka poor's man Para) should emit (relatively) collimated light if focused. That's where the ISL doesn't work. The focused look is a little harsh to my taste, but works great with large paras (like the 222) far from the subject. The "defocused" look is what the most people are after. It's like a huge ring light.
Long story short - if you try to defocus your para - the inverse square law will work again :)

Jacques Cornell's picture

I like the sunny look of my Paul C. Buff Extreme Silver 5' PLM. At a distance of 3'-5', the source is large enough to soften the light/dark transitions, yielding a look that's at once contrasty and less harsh than, say, a beauty dish. It's a pretty unique look and one that I like a lot.
P.S.: I suppose you could get a similar look from any large silver umbrella or undiffused softbox with a silver interior. But, you won't get the freedom from falloff with distance that a parabolic provides, and this is particularly helpful when shooting multiple subjects at different distances from the light. It also frees me from noticeable variations in exposure when my subject moves toward or away from the light, which, in turn, retains the key/background light ratio and saves me from having to selectively adjust brightness in post-production.
The one downside is that I have to be careful that subjects don't move off-axis, as the area lit is very tightly defined - with a 5' PLM, it's essentially a 5' circle at my working portrait distances.

Tammie Lam's picture

I'm with you here :) PLM is a legend. It's also almost parabolic, and for the price it's unbeatable.
Remember, PCB were making the on-axis shafts for their umbrellas (Balcar mount)? I don't understand why they aren't making them anymore... It's actually much harder to stay "on axis" with the umbrella mount.

Jacques Cornell's picture

I straighten out my speedlight and bungie it to the shaft. Works well enough. The Extreme Silver (no longer available) is so efficient I had to dial my monolight down to 15 Watt-seconds, and even that was too much at times, so a speedlight is more than enough.

Jacques Cornell's picture

The law applies to point sources radiating equally in all directions in empty space. As for diffused parabolics bring a "joke", it's only a joke if you don't know what you're doing. My PLM gives the option of focused, contrasty light without diffusion or the look of a normal softbox with diffusion, all without having to swap out the mod. To me, that kind of convenience in a high-volume production environment is certainly not a joke.
Modifiers that focus light most certainly DO render the ISL inoperative. With a truly collimated light source (and no atmospheric absorption), light intensity falls off NOT AT ALL with distance. My PLM is not truly collimated, but it does get me exposure on all subjects within my in-studio working range that varies by only 0.2-0.3 stops. If the ISL were in effect, exposure on a subject 6 feet from the source would be two full stops less than on a subject at 3 feet, and this property of parabolics is highly useful.

Jacques Cornell's picture

Semantics. I'm talking practical use and providing real-world examples. All you're doing is asking photographers to calculate the "apparent" location for sources as wildly different as bare tubes, softboxes with silver or white interiors, silver or white interiors, with or without grids, or any combination thereof, also beauty dishes, regular umbrellas, semi-parabolic umbrellas, focusing parabolic umbrellas, and lights with snoots. I don't know about you, but I don't have time to set all these up in my studio, measure them, calculate the angle of illumination at various working distances, and estimate the "apparent" location and light falloff with distance for every one of them, then consult my Filemaker database each time a subject moves.
FWIW, I actually did this with my PLM to better understand what I could expect from it at various distances. Doing the math was a real chore. IIRC, the "apparent" location of the light was something like 35 feet behind its physical location.
My point at the outset was that the actual mods that actual photogs rely on do not throw light in a way that yields an inverse square diminution of light intensity with distance from the actual (not "apparent") source in real-world environments. So, while the ISL is a useful concept, it should not be taken as a precise guide to how lights behave in a studio or on location.
At the very least, it should not be used as a rule of thumb for many setups whose "apparent" source is substantially different from the physical location.
Personally, I have neither the time nor interest to create an online tool to help photographers calculate "apparent" locations for various source/mod combinations. If you want to have a go at it, knock yourself out.

Dan Shea's picture

Jacques is Correct. True Parabolic reflectors send out parallel rays of light, similar to rays of sunlight. There is little to no fall off. The same effect is found when you reflect sunlight with a flat mirror. (Just try it for yourself) There is no falloff(depending on the flatness of the mirror.) Light does not dissipate. It's brightness falls with distance, from point sources, because there are less photons per unit area further from the source.

Shane Castle's picture

The best takeaway for ISL is how to move your light stand(s) in order to change the light intensity. Turns out that memorizing the f-stop numbers is not such a waste of time after all.