In technical terms, an inverse-square law is defined as “any physical law stating that some physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity.” With a definition like that, you’re probably wondering what on earth this could possibly have to do with photography (and no one could blame you). Inverse-square laws apply to many, many things in the world. Today however, we’re only going to be looking at one of them: light.
Explaining The Concept
For those of us without an intense knowledge of advanced mathematics (or even very basic mathematics for that matter) something such as the inverse-square law can seem incredibly daunting. There are equations with numbers and variables, references to physics and many more things which quite frankly seem very boring. For that reason we’re going to try to cover this in a very practical way, rather than a technical one.
The law itself, in photography, applies to lighting. It applies to any sort of lighting really but its most relevant application is with off camera lighting. In a nutshell, the inverse-square law teaches us how light works over distance and why the distance between your light source and your subject is so important.
Let’s say we have a light source which is on full power and our subject is 1 meter away it. If we move our subject double the distance away from the light (2 meters), how much of the light’s power will reach it? The natural reaction is to think “half power” – but unfortunately that’s now how light works, it follows an inverse-square law.
According to the law, the power of the light will be inversely proportional to the square of the distance. So if we take a distance of 2 and square it, we get 4, the inverse of which would be 1/4 or rather, a quarter of the original power – not half.
Moving our subject 3 meters from the light (3 * 3 = 9, so 1/9) the power of our light source now becomes 1/9th of what it originally was.
Here’s how the drops in light power work from 1 to 10 meters, remember that each one is simply the distance squared, over 1.
The inverse square law explains the dramatic drop-off in light over distance. We can use this information to better understand how our lights are affecting our subject and by that measure, how to control them better.
Putting It to Work
So knowing about light fall-off is fun and everything… but how can we put it to good use in our photography? Well, it’s all about exposure and relative positioning. When a light shines in a particular direction, initially the drop-off in light is very quick, then it slows down the further it goes.
Remember that with a square law, the numbers get bigger more and more quickly, however with an inverse square law the numbers get smaller more and more slowly.
If we look at our light drop-off from 1 meter to 10 meters in percentages to the nearest whole number, it would look like this:
There’s a 75% drop in light from 1 meter to 2 meters, but only a 5% drop in light from 4 meters to 10 meters.
Exposure
So we understand that there’s lots of power very close to the light source, but only a very small amount of power far away from it. On that basis, to get a correct exposure (assuming we use a consistent shutter speed), if the subject was very close to the light then we would need to set our aperture to around F16, to block out all the excess light.
If, on the other hand, the subject was very far away from the light, then we’d set our aperture to around F4 in order to let much more light in. Both photographs should look identical because we’ve adjusted our camera to let in the same amount of light for each one.
So on that basis, we can plot out a rough estimate of where all the correct F-Stops are to get a correct exposure level. Remember that the light drops off very fast at first, then slower. In the same way, we open up our aperture very fast to start with, then slow down the further we get away from the light.
Lighting One Subject
Let’s move those F-Stop reference numbers up to the top of our diagram as a handy point of reference. Now, some subjects don’t move, which means that once you place it a certain distance from the light source you set your exposure and that’s it.
However, if you’re shooting another person (especially a standing person) they have a tendency to move around. If your model is very close to your light source and she (or he) moves a half step in either direction then she’ll immediately be massively under or over exposed.
However if the model is further away from the light then she can move several steps in either direction without you needing to change any settings on your camera at all.
Lighting Groups
The previous rule works in a very similar way with groups of subjects. If you have all of your subjects very close to the light, then the one furthest away from the light will be very under-exposed compared to the one which is closest to it – covering the range from F22 all the way through to F11.
But if you move all the subjects away from the light source, then they become lit pretty evenly around F4.
Lighting Backgrounds
Of course sometimes you actually want one element of your photo to be bright and one to be dark, such as with a background. So, if you were to place your model very close to the light source with a backdrop some distance away, then (assuming your model is exposed correctly) the backdrop would be very under exposed.
If you instead wanted to have a bright subject with a bright background, then you would have both of them further away from the light source, but close to each other.
Conclusion
This has only been a very brief introduction to the inverse-square law as it applies to light sources in photography. There are many, many variables that can all be tweaked for different effects, such as shutter speed, the brightness of the light source, and adding multiple lights.
Hopefully however, you now understand the basics of the inverse-square law and you can start applying them to your photography to achieve better, more consistent lighting.
If you have any hot tips to help people out with understanding this subject, or anything else you’d like to share, then please do let us know in the comments below!
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By John O'Nolan
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Light fall-off made easy to understand + very informative graphics. Good work!
Agreed! The graphics made it much easier to understand. Awesome work.
Great post, thank you. This is really important, not only for photographers but for any designer and illustrator. I would love to see a similar post about shadows.
great! it’s muuuuch clearer now! thank you!
Nice explain, thx.
THANK YOU, THANK YOU, THANK YOU!!!!!
I cant tell how the relationship of the f-stops have frustrated the heck out of me lol This helps alot in moving on to a better understanding !!!
No problem – don’t forget that the f-stops discussed here are only correct in relation to a light source such as a flash or studio light though
Excellent!
The diagrams alone are worth the price of admission, even if there was no explanatory text. As far as I can tell, the math is correct, or at least, close enough for usefulness. (I suck at math, but I like pictures!)
Thank you for an instant favourite!
My pleasure Jeff, thanks so much for your comment!
John,
Did you make all those explanatory diagrams? Kudos to your for the amazing effort! Well certainly, these things are really confusing if you’re new to photography. But thanks to great authors like you, newbies and amateurs have now a whole new world to understand and comprehend the rules of photography.
Great article
I did indeed Rish! I’m really glad you found the article helpful, that’s what makes it all worth while! Thanks very much indeed for taking the time to leave such a great comment!
Great post. Really enjoyed your article and that you went way beyond the normal fare. I agree with the previous poster; awesome diagrams.
Thanks Rick, I’m genuinely thrilled that you both enjoyed the post! I guess I’ll have to write a few more like this?
Absolutely. This is exactly the sort of article I’d like to see here, great quality, single subject explained well, and absolutely excellent diagrams.
The only thing that would make this more interesting is some real world examples of the above diagrams – showing the same exposure and difference in light fall off, and then different exposures showing the same lighting because of the changed distances, if that makes sense.
Honestly though, that would just be icing on the cake.
Thanks for the feedback Jeff, that’s a great idea!
This is such a great article! Well written and easy to understand! Thank you so much! I’ll be linking back to this from my blog at http://ojphoto.blogspot.com
Thanks!
awesome!! exactly what i was looking a really long time.
Great article. I have to use this principle quite often when I’m doing quick and dirty off-camera flash work…especially at nighttime outside. It’s always a little bit of testing but keeping this in mind definitively helps.
Thats a very good article! I never thought that the light power drops THAT much. Youve made it very easy to understand light and the effects of distance, etc.!
Thank you very much
This is a very well written article with great graphics. I didnt really understand the inverse square law before reading your article and now I do! Thank you very much.
its good for me and for the beginer photographer. Credit to you and im linking to my blog site. Thank you
great illustration and very comprehensive explaination…can easily be understood, very useful for me. thanks
Photographers are visual people, and your charts were perfect in explaining the effects of the inverse square principle. Thanks for a great job. I’ll print out the charts, they really make it practical to use this important lighting lesson.
So if you’re trying to shoot lets say in the noon sun and it’s really bright and aperture is at 1.8, it’s going to be overexposed, correct? Theoretically, it’s going to be hard to get bokeh behind an object that is strongly lit?
Hi Ken,
That’s exactly correct yes. So this situation you have two options:
1.) Forget about using flash, once you take away the flash unit and sync speed limitations you can crank your shutter speed up to 1/4000 (for example) and get the bokeh you’re after.
2.) Compromise on all fronts: Reduce your ISO to below the normal sensitivity, if possible (depends on camera), increase your aperture a little, move closer to the subject. All these things will help marginally with a reduced exposure while maintaining bokeh in bright ambient light.
hey John, it was a clear useful article, I loved it, and your two points included in your comment above here.
It’s true you need to “compromise on all fronts” with a bit of experimentations to get the perfect thing.
Maybe it’s true for getting an ideal shot, is to test with different aperture F-Stops, shutter speeds, ISO settings, distance, multiplicity of light sources and light power, all that along with existent ambient light. Many thanks to u c; /
Excellent tutorial. Well explained and superbly illustrated. If I understand it as well as I think I do, then I need to use exposure priority more.
Awesome work.
I have looked at several pages on the Internet for a decent explanation of the Inverse Square Law and this is the best one! Simple without being patronising, clear and the diagrams are a huge help. I love this site anyway and have recommended it to readers of my blogs, so I hope you get more visitors. Keep up the good work!
I tried searching for keywords and didn’t find it, so hopefully no one brought it up yet… It’s a little late but hopefully someone reading this article might find this useful as well:
Think of light as having depth of field. The closer it is to the subject, the faster it falls off and loses power (relative to the subject). The farther away it is, the more depth it has and therefore is evenly lit for a longer distance.
- Strobist
such a great article – presentation and content are excellent. this is very helpful to me as a strobist photographer. tnx u so much for sharing.
Thank You so much. Good work!
What a great teacher you are…you went the extra mile in your “Putting it to Work” section with the diagrams which put everything (dry mathematical formula) into perspective…I absolutely salute your efforts and thank you so much…
after reading this several times in other sources, i have finally understood it with the help of these diagrams. thanks so much
Illustrated perfectly. The formula is easier to comprehend with the graphs. Awesome photography tutorial. Applying it with some hard lights.