ISL: its the Law

The inverse square law (ISL) is one of those things that just annoys me as I keep confusing myself after I've learned it. When you look at it, its quite simple.

The ISL states that for a point light source:

I = 1/r^2

where I = intensity and r = distance.

But how does it relate to lighting? Heres the deal..

The ISL can give us an indication of the intensity of the original light source given another distance.

We have to say 'indication' as the ISL uses a theoretical point light source which in practice, our lights can only very roughly approximate - and this is without the presence of light modifiers (softboxes/umbrellas/...) which further changes the way the original light source spreads and travels over distance.


Lets start off with the situation where our light source is powered such that at a given distance of 1 ft (r=1), a subject is exposed at f/11 (I=f/11).


Using our example numbers and the ISL, we can approximate the light intensity of a change to light-subject distance. Lets say we double our subject distance (such that r=2).

Substituting into the ISL, we get:

f/11 = I = 1/4 (r=2)

This states that for our original power, the intensity at 2x the original subject distance will be 1/4 of the original intensity. So, whats that in terms of something I understand (ie f/stops)? Thats 2 stops lower in intensity which translates to:

f/11 = I = 1/4 = f/5.6

Stated another way:

Doubling your subject distance, requires approximately 4x times the amount of light to bring back up to original intensity

Of course, the ISL can be applied to any change to subject distance.

So hows this help us with lighting? It means we can control and change lighting ratios quickly such as approximating how far a background needs to be from an previously exposed subject for it to be black (it needs 2 1/2 stops below working aperture).