The Inverse Square Law

The inverse square law is used when the photographer controls the light source, when he or she can control its strength and move it nearer or further from the subject.

It is a pretty simple calculation that enables you to know how much light is going to illuminate a subject and from the subject to your camera at a given distance.

Let’s start in a situation where you do not use the inverse square law.

That would be where you pretty much cannot control the light, such as when you are taking photos outside in daylight.

When the sun is in the sky and there are no clouds, then the sun is a specular light. That means it is a concentrated light source that will cause deep shadows and bright highlights.

True, the light from the sun is all over the sky but the light source itself (the sun) is a small light bulb in the sky and all the light is travelling straight from it.

That causes a lot of contrast with bright highlights and deep, harsh shadows when it strikes an irregular surface such as a human face, particularly older faces with cracks and crevices.

But a bright sun also casts shadows below noses and below foreheads, and it is not the most flattering light, except perhaps for older, craggy male faces.

It’s different when it’s cloudy.

The light from the sun is diffused as it scatters and bounces through the clouds. The range of intensity from light to dark is less, there are fewer shadows and everything blends more evenly.

The photo of the woman above was taken on a cloudy day, and there are no harsh shadows.

The California Sunbounce is a giant diffuser that a photographer can put above the head of a subject. And film makers with a crew behind them can use big lights to swamp the light of the sun.

But if you are just a photographer with a camera, there is not a lot you can do to affect the light of the sun.

Studio Flash

It’s different when you are taking photos indoors using a studio flash or continuous lighting.

You will probably diffuse the light through lightbox or you will bounce it off a reflector to make a more flattering, even light.

That’s when we need to know how to work with the light and know how to adjust it.

When you are working with flash the only variables you control are the ISO and the aperture.

The shutter speed is pretty irrelevant because the flash goes off at something like 1/2000th of a second. And that determines the length of time there is light on the subject.

This is where the inverse square law comes in. The law allows you to calculate how much light falls on a subject as the light source moves nearer to or further from the subject.

The law wasn’t dreamed up. It is not a convention. It is a law of physics derived from observations.

Everyone knows that when you move a light source away from a target, the light falls off. And it should surprise no one that the light falls off at a predictable rate.

The inverse square law tells you what that rate is.

Let’s start with a light that is a distance two metres (2m) from the subject, and the subject is adequately lit.

The only light source is the flash. Any other light source in the room will be drowned out by the flash when it goes off.

Now you move your flash from 2m to 4m from the subject. The amount of light hitting the subject is less because the light has to cover twice the distance,

The amount by which the light falls off is the inverse of the square of the distance.

So to light the subject to the same amount as the subject was lit at two metres, we must square the amount of light.

Now you want to know how to set your camera. And f-stops tell you exactly what to do.

Suppose the correct aperture was f16 when the light source was 2m from the target.

When the light is 4m from the target the aperture you have doubled the distance, so the light needs to be the square of doubling. That is, it needs to be four times stronger for the same amount of light to hit the target.

How do we know what aperture is four times stronger, meaning that it takes in four times as much light – as f16?

Well, that’s how f-stops were designed because every stop of light is a halving or doubling of the light.

Here is a range of f-stops from smaller to larger. The list covers most lenses you are likely to come across.

f32, 22, f16, f11, f8, f5.6, f4, f2.8, f2, f1.4, f1.0

So to push out four times the light at 4m as at 2m, we need to square it, which means we have to double the light (one f-stop) and double it again.

In our setup we were at f16, so we need to go 2 stops to f8.

That’s it.

If you move from 2m to 3m or from 6m to 9m, the math is a bit more complicated than when working with doubling or halving, but the light needs to be increased by 1.5 x 1.5 = 2.25 times and that equates to a bit over a stop – actually 1.17 f-stops.