The Inverse Square Law, explained

Most photographers using artificial lighting know about the Inverse Square Law, namely the fact that light intensity decreases according to the square of the distance between the light source and the subject. This is important for two reasons:

  1. The farther your subject is from the light source, the more power you must use to light it, and
  2. Light falls off more rapidly the closer you are to the light source, therefore you can easily make a background go dark by putting your light very close to the subject.

This is explained very clearly by David Hobby in his Ligthing 102 series:

You gotta lose the math. Here is what you need to know about the inverse square law: The closer you are to the light source, the more powerful the light. Get real close and it gets really powerful. Get far away, and it gets weaker.

And here’s the other thing: The closer you get to the light source, the quicker the lighting values change as you move in. When you get farther away, small differences in distance (from the light) become meaningless.

Pretty simple explanation, but you see, I am an engineer and sometimes I get a warm and fuzzy feeling from knowing all the intricate math details: I don’t wanna “lose the math” yet. So I thought about a way to explain the law in the simplest and easiest to apply terms, something that would not require the use of a pocket calculator. Here is the process that I came up with:

  1. Measure the distance between light source (L) and subject (S), call it LS.
  2. Measure the distance between light source and background (B), call it LB.
  3. Compute the LB/LS ratio and approximate it to the nearest f-stop.
  4. Count how many f-stops are there between f/1 and the value you computed in the previous step. This is how darker your background is with respect to your subject.

As an example, imagine that you are lighting Mary from one meter away, and that Susan is sitting 0.5m from the background, that is 1.5m from the light. Compute LB/LS = 1.5. Approximate to f/1.4, that is one stop below f/1, so your background will be one stop darker than Susan.

Want to have the background 2 stops below? Easy, put 1m between L and S, and 1m between S and B: LB/LS = 2. Want 5 stops? Put 1m between L and S and 5m (really 4.6m, but I wouldn’t go so far as to think in thirds of a stop) between S and B: LB/LS = 5.6. Easy, huh?