How the inverse square law works
Light from a point source spreads in all directions. At twice the distance the same light covers four times the area, so the illuminance on the subject falls to a quarter. At three times the distance it falls to a ninth. In formula form, the illuminance E equals the intensity I divided by the square of the distance d.
E = I / d²
In stops
One stop is a factor of two in light. A factor of two in light corresponds to a change of the distance by the square root of 2, about 1.41. Doubling the distance therefore costs two stops and halving it gains two stops. Moving a light from 2 m to 1.4 m adds one stop.
stops = 2 × log2(old distance / new distance)
Use in photography
For flash and continuous lights the law explains why a subject close to the light is much brighter than one further back, and why foreground and background differ in brightness. To change the light by one stop, move it by a factor of 1.41 in distance, for two stops by a factor of 2. The distance counts from the light source to the subject, not from the camera.
Limits
The law describes a point source. For a source of finite size with uniform luminance it is accurate within 1 % when the distance is at least 5 times the largest dimension of the source. A large softbox close to the subject therefore does not follow it exactly, and the field for the size of the light source warns when the distances are too short. Light that does not spread from a point, such as a parallel beam, is not described by it either.
FAQ
What is the inverse square law?
The inverse square law states that the illuminance on a surface from a point source falls with the square of the distance. Twice the distance gives a quarter of the light.
How many stops do I lose when I double the distance?
Two stops. A quarter of the light is two stops less.
How far do I move the light to gain one stop?
Closer by a factor of about 1.41, for example from 2 m to about 1.4 m. For one stop less, move it further away by the same factor, from 2 m to about 2.8 m.
Does the law apply to a softbox?
Only at distances that are large compared with the size of the softbox. The Illuminating Engineering Society gives a distance of at least 5 times the largest dimension of the source for an accuracy of about 1 %. Closer, the result is less accurate.
Does the law apply to sunlight?
The sun is so far away that a change of a few metres changes the distance by a negligible fraction, so the brightness of a scene does not change measurably.
Is the distance measured from the camera or from the light?
From the light source to the subject. The position of the camera does not matter for the falloff of the light.
Sources
- Illuminating Engineering Society: Glossary: inverse-square law