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How Light Works—The Inverse Square Law

Understanding the inverse square law can lead to better lighting in your photos
Every year in my studio photography class I give a lecture on the Inverse Square Law. With a name like that it doesn’t sound like it would be a laugh-a-minute romp, but in fact, the students are captivated! Well maybe not captivated, but they’re excited once they see how these laws of physics can be quite useful when it comes to lighting a subject—especially when working with studio lights.

You see, the inverse square law is the reason why you can read a book by candlelight so long as the candle and the text are fairly close together. Try dragging that book across the room and suddenly that once-bright candle will seem very dim by comparison. This is somewhat obviously because light falls off in intensity as it travels farther from the source. And this falloff is quantified with the inverse square law, which says that a light’s intensity is inversely proportional to the square of the distance. What good does knowing that do for you?

In practice, it means when the distance from the light doubles, the exposure falls off not just by one stop but by two. The light may be twice as far away, but it’s four times less powerful. Crazy, right?

It may help to view an illustration of this concept. Look at the drawing below, which shows the light spreading as it travels farther from the source. If you think of each photon of light as a tangible substance (like a tablespoon of peanut butter, for instance), it’s equivalent to spreading that same photon across a wider area, making it thinner in the process. To continue the analogy, it’s spreading the same tablespoon of peanut butter across not just one slice of bread but four. Double the distance again and it’s spread across 16 slices, and so on. That sandwich is going to be pretty thin on peanut butter in no time.

Understanding the inverse square law can lead to better lighting in your photos

So how does this manifest itself when it comes to photographic lighting? Simple. If your key light is, say, four feet from the subject and the correct exposure is ƒ/1, when you move the light 8 feet from the subject, the exposure will fall off by two stops, meaning your new correct exposure will be ƒ/5.6. The reverse is also true: If you know you’d like to get from ƒ/5.6 to ƒ/11 simply by moving the light, you know you’ll have to halve its distance from the subject. With this knowledge, you can quickly make accurate adjustments when you’re fine-tuning a lighting setup.

The other way this law of physics can benefit your lighting is when it comes to using the falloff creatively in your pictures. Position a key light close to a subject—say, 18 inches away—and the light will fall off very quickly across the scene. In practice, that means if you’d like the background to go dark, you should put your key light closer to the subject and position the subject farther from the background. This way, the light will fall off by two stops with every doubling of the distance—so it will be two stops under by the time it’s 18 inches beyond the subject and four stops under at 6 feet from the light, and so on.

Don’t forget the reverse is true here too. If you wanted that background to be as light as possible without a background light, you’ll want to position the subject closer to the background and the key light farther from the subject. In this way, when you expose correctly for the amount of light illuminating the subject from, say, 10 feet away, the background a foot and a half behind the subject will be brightly illuminated by the key light. This is because, with the key 5 feet from the subject, it would require the background to be 5 feet behind the subject to fall off two stops. (At 2.5 feet it’s only a half stop underexposed, so at 18 inches behind the subject it’s barely a quarter-stop underexposed—and that’s practically nothing.)

These techniques can be powerful ways to use a single light setup while still maintaining control over the brightness of the background relative to the subject, and it’s all done by changing the distances between background, subject and light. It works thanks to the utterly captivating physics behind the inverse square law.

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