A Quick Explanation of The Inverse Square Law

In a separate post, I mentioned how distance can be used to change the size of your light source. Distance also affects the power, or intensity, of your light. I'm talking about a rule you may have heard of called the Inverse Square Law. You know this rule intuitively. If you're reading a book by the light of a single lamp, you know you'll see the pages better if you get closer to the lamp. The closer you are to the lamp, the more intense the light will be on the pages of your book. That's the Inverse Square Law in action.

In a nutshell, the Inverse Square Law says that the power of your light is equal to 1/distance-squared, distance being a constant unit of measurement in your scene. At a distance of "one," the power of the light is 1/1, or 100% power. At a distance of "two," the power of the same light is 1/4 (2x2=4), or 25% power. At a distance of "three," the power of the same light is 1/9 (3x3=9), or about 11% power.

The distance can be any distance so long as the distance between "one," "two," "three," and so on is a constant unit. The diagram below will make this concept more clear.

If your head is spinning, just keep going. The photo examples will make everything click.

The Inverse Square Law in Action - Photo Examples

In the example I'll share below, I moved my light in increments of four-feet. That means the light in my first photo (four feet from my model) is a distance of "one." When I moved my light from four-feet to eight-feet away for my second photo, then the light in my second photo is a distance of "two." In the last photo, my light was 12-feet away, or a distance of "three."

I know, again we're getting a little bogged down in numbers. The photos will help, I promise. All of these photos were created with a Canon 6D and a Canon 100mm lens at f/10, 1/160, ISO 100. I used two flashes for my softbox, both of which were set to 1/2 power and 24mm zoom. For each photo, the only thing that changed was the distance. All settings remained the same. The photos are also straight-out-of-camera, no adjustments made at all.

Here's distance "one" (four-feet). That's 100% power for my camera and light settings.

Here's distance "two" (eight-feet). According to the Inverse Square Law, that's 25% of the light compared to the first photo. I didn't change any settings on my light or camera. I only changed the distance of the light source.

Here's distance "three" (twelve-feet). According to the Inverse Square Law, that's about 11% of the light compared to the first photo. Again, I didn't change any settings on my light or camera. I only changed the distance of the light source.

See how clearly distance affects the power of a light source? (And notice how the distance also affects the color of the background? Using distance to your advantage is one way you can turn a white wall to gray or black.)

Just to help you see the difference again, here are the three photos side-by-side:

For this tutorial, I didn't want to change the light output to adjust the exposure when the light got farther away because we can't always change the light output of our source. With a window or reflected light from a wall, we can't adjust the power. However, we can adjust the distance of our subject. When you can't change the output of your light source, the process just works in reverse: you move your subject instead of your light.

You might be curious about what the photos look like in comparison when exposed properly. Rather than adjusting in camera, I just changed the exposure in Lightroom. The third photo was almost 3-stops underexposed. Here's what the first and third image look like side-by-side when adjusted for exposure:

Using the Inverse Square Law

How is an understanding of the Inverse Square Law useful when creating photographs? Here's one way to use the Inverse Square Law to your advantage:

If you're lighting a big group of people, and your light is directional and not front light, then you'll have a noticeable difference in brightness when comparing the people closer to the light and farther from light. Just back up your light source, and your group will be more evenly lit. (You'll have to change your camera settings to account for the power loss due to distance.)

Don't be scared by the Inverse Square Law. You know how it works because your brain has experienced light and shadow for your entire life. All you need to do is use the rule to your advantage when thinking about light intensity and distance.

This article is one part of a three-part series on light. The other two articles can be found here and here.

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