Inverse square law.

The mathematical law which describes light falloff owing to distance.

Light dropoff from a light source always seems very rapid. Consider a campfire at night - a pool of light surrounded by darkness. Or a flashlight (electric torch in the UK) being shone into the night sky - a bright bar of light that rapidly fades to nothing. You might think that when you double the distance from a light source you get half as much light, but it doesn’t work like that - you actually get just a quarter as much light.

Space is three dimensional, so imagine a sphere drawn around a light source that’s producing photons. As you get further away from the light source this imaginary sphere increases in size. The surface area of the sphere also increases, but it’s being illuminated by the same amount of light - the same number of our photons. It’s not a simple 1:1 relationship - the sphere is not twice as large when you get twice as far from it.

The actual relationship between distance from the light source and size of the imaginary sphere can be described mathematically as the inverse square law. It states that light output is proportional to the inverse square of the distance. (ie: divide 1 by the distance, then square the result) So if you double the distance you get 1/2 ², or one quarter as much light. If you quadruple the distance you get 1/4 ², or only one sixteenth as much light.

All light sources* follow this rule, which is why light from a camera’s flash unit tends to drop off in intensity pretty rapidly. It also explains why you don’t necessarily gain much more flash range when you buy a moderately more powerful flash unit, and why foreground objects are much more brightly illuminated by your camera-mounted flash unit than distant objects.

* the one exception being collimated light of the type produced by lasers. Collimated light has light waves which are precisely parallel and do not spread out - and so such light does not follow the inverse square law.

cf. collimated light, flash unit, laser.

Entry last updated 2002-04-18. Term 664 of 1487.

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