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The Inverse Square Law

What it means to Photographers

It's useful to know a little about the inverse square law especially when using flash or studio lights. Basically all the inverse square law says is that an object that is twice the distance from a point source of light will receive a quarter of the illumination. So what it means to us photographers is that if you move your subject from 3 meters away to six meters away, you will need four times the amount of light for the same exposure. This can most easily be achieved by opening the lens aperture two f-stops (see aperture for an explanation) or using a flashgun that is four times as powerful.

What do we mean by a point source of light? Well in Physics there might be a very strict definition but for our purposes any flashgun or lamp can be considered a point source. The other variable to be aware of is that the law works for 'unfocused' light sources. Light from a laser or other highly focused source will not drop off quite so rapidly.

The reason why the power of the light diminishes so rapidly is not because it 'runs out of energy' or anything like that, but because it spreads and so a smaller and smaller proportion of the light hits the object. Here's a little diagram to illustrate the point.

The Inverse Square Law

As you can see from the diagram the beam of light fans out quite quickly and the object furthest from the light receives only a small proportion of the light, most of the beam misses the target.

The more the beam is focused the higher proportion of the light will fall on the object. With a theatrical spotlight for instance which has a very narrow beam, much more light will fall on the object.

In photography though we don't tend to use highly focused beams as they produce a very harsh light, too contrasty for our purposes. So the inverse square law, as a rule of thumb, works very well for us.

So why do we need to know this?

If you are using flash on camera and everything is automatic then you don't need to worry about it at all. Except you may 'run out of light' because your flashgun is not powerful enough. It also explains the big difference in exposure between objects or people near the camera and those only a few feet further away.

If you have read my tutorial on flash photography though you will know that I consider 'flash on camera' as one of the cardinal sins of photography, and should only be used in extreme emergencies. If your flash, or light source, is off camera or bounced off a wall (see flash photography for and explanation) then you have independent control over the distance from the light to the subject. In the studio my lights are often much closer to the subject that my camera. There are two reasons for this, one is to get more light on the subject, and the other is that the nearer the light is to the subject the less of a 'point source' it will be and so the softer the shadows will be on the subject.

All we really need to know

An automatic camera will do all the maths for you so, unless you are using manual exposure, you don't need to worry too much about the details. It is very useful though to have some understanding of what is going on so that it doesn't come as a surprise when you see the effects of all this in under or over exposed photos. Just remember 'at twice the distance, a quarter of the light reaches the subject'.

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