Applying the Inverse-Square Law to Photography Lighting

Don’t worry, this isn’t going to turn into a maths class, or a lecture on physics. It’s an old adage that photographers work with light and understanding a little about how light affects your scene is a useful thing to know.

In reality, you don’t have to be able to carry a headful of fractions and do mental arithmetic, just know that light has some interesting properties as it travels from its source, to your subject. This brings us to the inverse-square law.

This law applies not only to light but any physical quantity, but for our purposes it states that the intensity of a light source is inversely proportional to the square of the distance from that light source. Reading that you may be tempted to click the back button, but bear with us.

The actual formula reads: intensity of light = 1/distance2. So why is that worth worrying about? Those who are new to using light sources such as flashes and studio lights are likely to imagine that if you place a subject next to a light source and take a photo, then move the light twice the distance from the subject and take another shot, the light will be half as powerful. This is not the case because of the way light falls off using the inverse square law. To sum it up we have a diagram that lays out the values and intensities you will encounter as you move your subject away from a light source.

We have a theoretical light source set at full power and a subject who starts at 1m away from the light. If you use the formula and take the distance of 1 and square it you get 1 (1 x 1 = 1 so 1/1 intensity).

Move your subject to 2m and rather than the intensity being half power the formula tells us otherwise (2 x 2 = 4 so 1/4 intensity). At double the distance from the light source, the intensity is actually 1/4 the brightness or 25 per cent.

At 3m (3 x 3 = 9 so 1/9 intensity) it is now 1/9 or 11 per cent (we’ve rounded up the numbers) and so on.

Whilst this is all well and good, how does it help us in the real world? If you look at the percentages, from 1m to 2m, there is a 75 per cent drop in intensity. From 3m to 6m there is only an 8 per cent drop in intensity. Finally, from 6m to 8m – 10m, there is only a 2 per cent drop in intensity. We’ve added an approximate set of f-stops to show how you would alter your aperture to get a good exposure as the light intensity drops away the further your subject is from the light source.

Now we can put all this information together for some lighting examples.

Scenario 1

Your subject is very close to the light source. If they happen to move one step away from the light, they will be underexposed by a fair margin and you will have to alter your settings to compensate.

Scenario 2

Your subject is much further away from the light source. If they move a step in either direction this time, because of the much smaller fall off in intensity this far out from the light source, you will most likely not have to alter your settings at all.

Scenario 3

You have two subjects a very short distance from your light source, one of which is standing closer to the light than the other. The one further from the light source will be underexposed by a large margin due to the rapid fall off in the first few metres.

Mark Frost

Mark started work as a commercial artist during the good old days of Letraset, spray mount and having to process your photos at a local chemist. Having discovered his passion for photography, Photoshop and the wonders of digital image manipulation, he has not looked back. He is well on his way to owning more cameras than he’s had hot dinners.

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