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I hear photographers talk about the inverse-square law, particularly with reference to lighting.

What is this law about, and most importantly, how is it applied to lighting for photography?

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2 Answers 2

up vote 16 down vote accepted

The law states:

If you double your distance from a light source, the amount of light reaching you drops to a quarter of what it was.

More generally:

If you multiply your distance from a light source by X, the amount of light reaching you will drop by a factor of X^2 (X squared)

As is often the case, Wikipedia explains this very nicely (with a nice graphic, too).

Use for photographers

This means that you don't have to move very much relative to your light source in order to see a big change in the amount of light.

So, if you are lighting a subject with a strobe, you only have to move the strobe a little closer or further away to achieve a big difference in the amount of light reaching the subject.

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Good explanation! –  Johannes Setiabudi Aug 2 '10 at 22:26
    
also, since one "stop" is a doubling of the amount of light, and doubling the distance between light and subject cuts the light by 1/4 (2 squared), doubling the distance between light and subject is "2 stops". Nota bene, though: the rule doesn't necessarily apply with focused light. It applies completely to a point light source (because it's isotropic -- en.wikipedia.org/wiki/Isotropy)... with other sources, it's different (the extreme counter-example being a laser)... at least in abstract theory. In practical theory, it still applies, but the "distance" is non-obvious. –  lindes Dec 3 '10 at 21:47
    
Another practical effect is that the power of two given flash guide numbers can be compared by calculating the ratio of the square of those two numbers. –  mattdm Mar 26 '11 at 4:22
    
The rule also fails with large light sources (softboxes, scrims) until the subject is far enough from the light source for it to begin to resemble a point source. Very close, the fall-off is almost non-existent since the outer reaches of the source are able to illuminate areas they couldn't "see" before as the subject moves away, then there is an area where the light fall-off is directly proportional to the distance. Once you get to about twice the longest dimension of the source away, the inverse-square rule is pretty much in effect again (but your source is no longer very soft). –  user2719 Mar 26 '11 at 4:33

The inverse square is the proportion between the light intensity and the distance to the light source. At double the distance, the light is one fourth (1/2*2).

This applies to anything that spreads in all directions from a source, as the area of a sphere is proportional to the square of the radius.

So, if you move a lamp/flash away from the model, the light is reduced by the square of the distance. If you move the lamp from 1 meters to 2 meters, the light gets two stops weaker (1/2*2 = 1/4). If you move the lamp from 1 to 3 meters, the light gets a little more than three stops weaker (1/3*3 = 1/9).

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