An Introduction to the Inverse Square Law - Digital Photography School

An Introduction to the Inverse Square Law

I don’t know about you, but I was never much of a math student.  I needed a tutor in high school for both geometry and physics.  I chose a double major in college (Journalism/English) that required no math.  I practiced law for fourteen years, where any math I needed was either pretty easy or done on a calculator.  Even when I ditched my briefcase for a camera bag and embarked on a new career, I felt pretty secure in the knowledge that confusing math had no place in the world of photography.

And then the Inverse Square Law reared its ugly head.

It didn’t jump out and attack me right away.  No– the Inverse Square Law is much too cunning for that.  It was patient.  It bided its time.  It waited for me to get comfortable in my new skin a professional photographer.  It waited for me to feel secure in my knowledge and execution of studio lighting and off-camera flash.  And then it showed itself.

We all deal with light.  It is the defining element of what we do.  We capture light in a box and use it to tell a story.  Some photographers put themselves in the “natural light” category, while others work their magic with a firm grasp of off-camera flash.  While the Inverse Square Law comes into play more often with strobes, it is absolutely a concept that applies to every light source, and therefore affects every photographer.

So, what is it?  In all of its overly technical glory, the Inverse Square Law– as it applies to photography– is an equation that relates the intensity of a light source to the illumination it produces at any given distance.

Huh?

Regardless of how you classify yourself as a photographer, you already know that light travels.  It can be diffused.  It can be reflected.  It can be deflected.  But it travels.  This means that over time and distance its intensity can and will diminish.  What does that mean for your photography?  It means that doubling the flash-to-subject distance reduces the light falling on the subject to one-quarter.  Logically, we might assume that doubling the distance would reduce the power by half.  In actuality, however, doubling the distance reduces the power by 75%  More simply put, the Inverse Square Law is used (among other things) to determine the fall-off– the difference in illumination on a subject as it moves farther away from the light source.

Let’s take a look at a graphic that will help us get our heads around this.  We are looking at a blank wall approximately ten feet long, illuminated with a single light source.  Meter readings along the wall show the progression of one-stop increments.  Notice how we move one stop from f/22 to f/16 in a matter of inches, yet we move one stop from f/4 to f/2.8 over the course of a few feet.

The Inverse Square Law relates the intensity of a light source to the illumination it produces at any given distance.

The Inverse Square Law relates the intensity of a light source to the illumination it produces at any given distance. One-stop increments are spread over a wider area the farther the light travels.

Now that we understand what the Inverse Square Law is and how it affects the intensity of light, how do we apply it to our photography?  Let’s assume that we are photographing a family of four on our wall.  If we position them closer to the light– let’s say in the f/8 – f//11 range– we are going to have a lot of contrast between the subjects.  Those closer to the light source catch the brunt of the light and may be overexposed, while those further from it could be underexposed.  The variance in the light over such a short distance means the light falling on our subjects will be very uneven.  If, on the other hand, we move our family down the wall to the 7- or 8-feet mark, we have a wider area in which to achieve a more even exposure across the group.

Remember, though, that the same principles apply not only to our subjects, but to the relationship between the light source and the background as well.  If we are photographing our imaginary family with a plain white wall for a background, simply moving them closer to or farther away from the wall will affect whether the wall appears white, gray, or even black.

So far, we’ve discussed what the Inverse Square Law is and how it applies to off-camera flash.  But what about natural light?  The same concept applies, whether you are using window light, a reflector, a sunset, or any other non-electrical light source.  The principles of how light travels do not change just because the light in question has no batteries.  Doubling your subject’s distance from the window, for example, is going to result in the same 75% drop in intensity that you will experience with strobes or speedlights.

So, what’s the bottom line?  The best advice I can give about the Inverse Square Law is to simply be aware of it and understand its potential impact on your photos and lighting setups.  The more you understand light and how it behaves, the better equipped you will be to efficiently compose and create consistent images with less trial and error.

 

Read more from our Tips & Tutorials category.

Jeff Guyer is a commercial/portrait photographer based in Atlanta, GA. Still an avid street photographer and film shooter, Jeff also launched a kids photography class ("Digital Photo Challenges") three years ago. You can check out more of his work at Guyer Photography, and follow him on Facebook and Twitter.

  • someone

    very interesting indeed – now there’s another thing to think about amongst a bizillion others when taking a photo!

  • Bruce Douglas

    My favorite use of the inverse square law is for when there is no good position to light someone without getting a reflection in their glasses (some glasses just reflect everything!).
    If I put a softbox right on the edge of the frame, it will reflect but with a soft transparent reflection you can see the person’s eyes through. The principle is simple, the reflection is always the same intensity whether near or far but the light is much stronger so you can then stop down and the reflection gets quite soft.
    http://ak1.picdn.net/shutterstock/videos/1290508/preview/stock-footage-portrait-of-smiling-woman-with-glasses.jpg
    http://www.fredascott.com/data/photos/1171_1bc5b2359optresiz.jpg

    It also works well for wine bottles- the reflection is there but it’s soft and translucent:
    http://www.fullsteam.com/assets/example_resources/assets/80/medium_Ventana-bottles.jpg?1254175866

  • http://www.cramerimaging.com Pocatello Photography, Cramer Imaging

    I’ve got a portrait gig coming up this week where I’m shooting indoors with a backdrop. Thanks so very much for the post. You have helped me figure out where I’m going to position my gear.

  • Ed

    The thing I don’t get here is that sunlight is coming from so far away the diffusion should be so great that distance from the source shouldn’t matter much. Why does it?

  • http://www.jeffguyerphotography.com Jeff Guyer

    Ed– If you are photographing out in the open, you’re absolutely correct. The ISL is going to come into play, however, any time you try to shape or direct the sunlight. One way of looking at it is whether you are putting anything in between your subject and the sunlight. Windows, doors, reflectors, bounce cards, etc., essentially become a new light source once the sun hits them.

  • Ed

    Thanks Jeff.

  • Barry E Warren

    Thanks for the Great lesson on Inverse Square Law. This is very helpful since I’ve just got into using Speed Lights in some of my work.

  • http://blogs.gonomad.com/traveltalesfromindia/ Mridula

    Thanks for putting it so simply.

    http://blogs.gonomad.com/traveltalesfromindia/

  • http://bit.ly/oufr4c Brian Fuller

    If I had known that math was a big part of photography, I probably would have begun the hobby much sooner.

    Flickr:
    http://bit.ly/oufr4c

  • http://zain.zenfolio.com Zain Abdullah

    Thank you so much for the enlightenment..

  • Stuart

    Good practical tips, without too much theory!

    But I think it would be clearer to attribute the origin of the law to the fact that light spreads out rather than to the fact that it travels. Light from lasers and focused spotlights also travels, but does not spread out (much), and the law does not apply to light from such sources.

    Light that does spread out does so over an area — and area is measured by multiplying the length of two sides. If the the sides are the same length, then that multiplication amounts to squaring the number. Since light from a point source spreads out equally in all directions, the sides of an imaginary area at any distance from the source are equal, and the squaring applies. Here’s a graphic explanation: http://tinyurl.com/l35axcl

    It’s called an “inverse” law, because it takes the form “the more the [something], the less the [something else]” — in this case, the more the distance, the less the intensity of the light that falls on your subject.

    So, multiply the distance by 2, and the light gets spread out over 4 times the area and the intensity is reduced to 1/4 (one over two squared). Triple the distance, and the light gets spread out over 9 times the area and the intensity is 1/9 (one over three squared) of the original strength. And so on.

  • John Curlett

    I think it would be helpful to add some additional explanation here. The inverse square law says that the light intensity of a point source of light, radiating in all directions in space with nothing to obstruct or reflect the light will decrease by the square of the distance. This law does not accurately define the light fall-off from common light sources like flashlights, car headlamps and most of the lighting we use in photography because the light is focused to some extent causing the light intensity to fall-off at a lower rate. It defines the worst case which is approached when using bare bulb flash. The more focused the light, the slower the light intensity falls off (a laser pointer is an extreme example). Understanding that the amount of light fall-off is different depending on the light source and modifier is important in photography. An example is lighting a subject in front of a back-drop with a single light source. Keeping the locations of the flash, subject and backdrop and the exposure at the subject all the same, the light illuminating the backdrop will be much brighter if the light modifier is a parabolic reflector as compared to a soft box. Add a grid to the reflector and the difference will be more. I hope this helps answer some questions that arise when your results are not exactly what you expected.

  • ArturoMM

    stuart:

    Good point, it’s the spreading not the traveling what reduces the intensity.

    And the graphic is very understandable.

  • Fritz

    I think you are simplifying too much while trying to make your story easy to understand.

    The intensity of light decreases when a light bundle gets wider. When the light rays go parallel, like a laser, the intensity remains (almost) the same.

    The rays of the sun are parallel, so there is no negative square law at play.

    When you use your flash outdoor, in the dark!, the law applies very well.

    When you you use your flash indoor, the law applies not very well because light rays bounce from walls, ceiling etc. It applies better in a large room than in a small room.

    When the light source is big (softbox), it doesn’t apply very well either.

    So, it all depends :-).

    Still, it is good to know how light behaves, and the negative square law is part of it.

    In the past, we had to understand this perfectly. Nowadays, we can check our photograph immediately and try again if the picture is not good.

  • anotherview

    Technology has caught up with part of the problem producing unsharp photographs taken using a DSLR. Adobe has introduced a new sharpness filter with its release of Photoshop Creative Cloud. This filter analyzes a digital photograph for the slight blurring effect that occurs in many digital photographs. The filter then removes this blurring, thereby sharpening the photograph more true to the optical qualities of a given lens. You have to see this de-blurring effect to appreciate it.

    Note that the DSLR mirror-slap action induces a minute vibration into the camera which results in a slight blurring effect barely visible in the photograph . This blurring will happen whether or not the photographer uses a tripod or a remote shutter release.

    The remedy, not mentioned in the article, involves locking up the mirror. The DSLR has a setting for mirror lockup. Once set, the shutter requires two actuations. The first one moves the mirror out of the light path, and locks it in place. The second one releases the shutter to expose for the scene.

    Between the first and second shutter actuation, the minute vibration from the mirror-slap dies down. This dying-down takes about 2 or 3 seconds, at most. You can see the minute vibration itself by mounting a bubble level in the DSLR hotshoe, and watching it when doing the first shutter release. The bubble moves a little. For this test, you will of course have to mount the DSLR on a tripod.

    Note that IS continues to work with the mirror locked up. In my experience, IS does not compensate for blur in photographs caused by mirror-slap.

    I have not yet experimented with hand-holding my DSLR with the mirror locked up and IS turned on to determine if this setting combination avoids blur in the photograph. It should, though.

    As to hyper-focal distance use, I’ve been employing the rule of thumb of focusing on a point about one-third of the way into the scene in the frame in the viewfinder. This technique nearly always achieves sharp focus from near to far.

    To facilitate this HF technique, I manually set the Auto-Focus point to the lower position viewed in the frame, whether in Landscape or Portrait mode. Doing so controls where the lens focuses in the frame. This focus point comes very close to the HF distance, but I adjust where the AF point rests in the scene as needed. Try this technique yourself to see the results.

  • Rafi Markus

    Hi,
    The explanation is perfectly clear. What I am wondering about, now, is how does this effect the intensity of the flash.
    How many steps should the intensity of the flash be increased to get the same intensity of illumination when the distance to a subject is doubled?
    How much is this intensity increased by each step?
    Thanks,
    Rafi

  • Mary

    Novice here. This is a great example. Thank you. My dilemma is that I have a volleyball team that I have to photograph as a group and individuals. It is indoor the lighting is coming from the ceiling, and I had horrible shadows the last time I did this. What do you suggest in this case?

  • http://www.jeffguyerphotography.com Jeff Guyer

    Mary– send me an email and I’ll point you in the right direction.

Some older comments

  • Jeff Guyer

    September 8, 2013 01:42 am

    Mary-- send me an email and I'll point you in the right direction.

  • Mary

    September 7, 2013 10:44 pm

    Novice here. This is a great example. Thank you. My dilemma is that I have a volleyball team that I have to photograph as a group and individuals. It is indoor the lighting is coming from the ceiling, and I had horrible shadows the last time I did this. What do you suggest in this case?

  • Rafi Markus

    August 23, 2013 04:55 pm

    Hi,
    The explanation is perfectly clear. What I am wondering about, now, is how does this effect the intensity of the flash.
    How many steps should the intensity of the flash be increased to get the same intensity of illumination when the distance to a subject is doubled?
    How much is this intensity increased by each step?
    Thanks,
    Rafi

  • anotherview

    August 23, 2013 03:35 pm

    Technology has caught up with part of the problem producing unsharp photographs taken using a DSLR. Adobe has introduced a new sharpness filter with its release of Photoshop Creative Cloud. This filter analyzes a digital photograph for the slight blurring effect that occurs in many digital photographs. The filter then removes this blurring, thereby sharpening the photograph more true to the optical qualities of a given lens. You have to see this de-blurring effect to appreciate it.

    Note that the DSLR mirror-slap action induces a minute vibration into the camera which results in a slight blurring effect barely visible in the photograph . This blurring will happen whether or not the photographer uses a tripod or a remote shutter release.

    The remedy, not mentioned in the article, involves locking up the mirror. The DSLR has a setting for mirror lockup. Once set, the shutter requires two actuations. The first one moves the mirror out of the light path, and locks it in place. The second one releases the shutter to expose for the scene.

    Between the first and second shutter actuation, the minute vibration from the mirror-slap dies down. This dying-down takes about 2 or 3 seconds, at most. You can see the minute vibration itself by mounting a bubble level in the DSLR hotshoe, and watching it when doing the first shutter release. The bubble moves a little. For this test, you will of course have to mount the DSLR on a tripod.

    Note that IS continues to work with the mirror locked up. In my experience, IS does not compensate for blur in photographs caused by mirror-slap.

    I have not yet experimented with hand-holding my DSLR with the mirror locked up and IS turned on to determine if this setting combination avoids blur in the photograph. It should, though.

    As to hyper-focal distance use, I’ve been employing the rule of thumb of focusing on a point about one-third of the way into the scene in the frame in the viewfinder. This technique nearly always achieves sharp focus from near to far.

    To facilitate this HF technique, I manually set the Auto-Focus point to the lower position viewed in the frame, whether in Landscape or Portrait mode. Doing so controls where the lens focuses in the frame. This focus point comes very close to the HF distance, but I adjust where the AF point rests in the scene as needed. Try this technique yourself to see the results.

  • Fritz

    August 23, 2013 09:24 am

    I think you are simplifying too much while trying to make your story easy to understand.

    The intensity of light decreases when a light bundle gets wider. When the light rays go parallel, like a laser, the intensity remains (almost) the same.

    The rays of the sun are parallel, so there is no negative square law at play.

    When you use your flash outdoor, in the dark!, the law applies very well.

    When you you use your flash indoor, the law applies not very well because light rays bounce from walls, ceiling etc. It applies better in a large room than in a small room.

    When the light source is big (softbox), it doesn't apply very well either.

    So, it all depends :-).

    Still, it is good to know how light behaves, and the negative square law is part of it.

    In the past, we had to understand this perfectly. Nowadays, we can check our photograph immediately and try again if the picture is not good.

  • ArturoMM

    August 23, 2013 03:09 am

    stuart:

    Good point, it's the spreading not the traveling what reduces the intensity.

    And the graphic is very understandable.

  • John Curlett

    August 23, 2013 03:07 am

    I think it would be helpful to add some additional explanation here. The inverse square law says that the light intensity of a point source of light, radiating in all directions in space with nothing to obstruct or reflect the light will decrease by the square of the distance. This law does not accurately define the light fall-off from common light sources like flashlights, car headlamps and most of the lighting we use in photography because the light is focused to some extent causing the light intensity to fall-off at a lower rate. It defines the worst case which is approached when using bare bulb flash. The more focused the light, the slower the light intensity falls off (a laser pointer is an extreme example). Understanding that the amount of light fall-off is different depending on the light source and modifier is important in photography. An example is lighting a subject in front of a back-drop with a single light source. Keeping the locations of the flash, subject and backdrop and the exposure at the subject all the same, the light illuminating the backdrop will be much brighter if the light modifier is a parabolic reflector as compared to a soft box. Add a grid to the reflector and the difference will be more. I hope this helps answer some questions that arise when your results are not exactly what you expected.

  • Stuart

    August 23, 2013 02:40 am

    Good practical tips, without too much theory!

    But I think it would be clearer to attribute the origin of the law to the fact that light spreads out rather than to the fact that it travels. Light from lasers and focused spotlights also travels, but does not spread out (much), and the law does not apply to light from such sources.

    Light that does spread out does so over an area -- and area is measured by multiplying the length of two sides. If the the sides are the same length, then that multiplication amounts to squaring the number. Since light from a point source spreads out equally in all directions, the sides of an imaginary area at any distance from the source are equal, and the squaring applies. Here's a graphic explanation: http://tinyurl.com/l35axcl

    It's called an "inverse" law, because it takes the form "the more the [something], the less the [something else]" -- in this case, the more the distance, the less the intensity of the light that falls on your subject.

    So, multiply the distance by 2, and the light gets spread out over 4 times the area and the intensity is reduced to 1/4 (one over two squared). Triple the distance, and the light gets spread out over 9 times the area and the intensity is 1/9 (one over three squared) of the original strength. And so on.

  • Zain Abdullah

    August 22, 2013 05:42 pm

    Thank you so much for the enlightenment..

  • Brian Fuller

    August 22, 2013 04:41 am

    If I had known that math was a big part of photography, I probably would have begun the hobby much sooner.

    Flickr:
    http://bit.ly/oufr4c

  • Mridula

    August 22, 2013 02:58 am

    Thanks for putting it so simply.

    http://blogs.gonomad.com/traveltalesfromindia/

  • Barry E Warren

    August 22, 2013 01:34 am

    Thanks for the Great lesson on Inverse Square Law. This is very helpful since I've just got into using Speed Lights in some of my work.

  • Ed

    August 22, 2013 12:54 am

    Thanks Jeff.

  • Jeff Guyer

    August 22, 2013 12:42 am

    Ed-- If you are photographing out in the open, you're absolutely correct. The ISL is going to come into play, however, any time you try to shape or direct the sunlight. One way of looking at it is whether you are putting anything in between your subject and the sunlight. Windows, doors, reflectors, bounce cards, etc., essentially become a new light source once the sun hits them.

  • Ed

    August 21, 2013 10:53 pm

    The thing I don't get here is that sunlight is coming from so far away the diffusion should be so great that distance from the source shouldn't matter much. Why does it?

  • Pocatello Photography, Cramer Imaging

    August 21, 2013 12:01 pm

    I've got a portrait gig coming up this week where I'm shooting indoors with a backdrop. Thanks so very much for the post. You have helped me figure out where I'm going to position my gear.

  • Bruce Douglas

    August 21, 2013 10:02 am

    My favorite use of the inverse square law is for when there is no good position to light someone without getting a reflection in their glasses (some glasses just reflect everything!).
    If I put a softbox right on the edge of the frame, it will reflect but with a soft transparent reflection you can see the person's eyes through. The principle is simple, the reflection is always the same intensity whether near or far but the light is much stronger so you can then stop down and the reflection gets quite soft.
    http://ak1.picdn.net/shutterstock/videos/1290508/preview/stock-footage-portrait-of-smiling-woman-with-glasses.jpg
    http://www.fredascott.com/data/photos/1171_1bc5b2359optresiz.jpg

    It also works well for wine bottles- the reflection is there but it's soft and translucent:
    http://www.fullsteam.com/assets/example_resources/assets/80/medium_Ventana-bottles.jpg?1254175866

  • someone

    August 21, 2013 07:10 am

    very interesting indeed - now there's another thing to think about amongst a bizillion others when taking a photo!

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