The dreaded inverse square law (it’s so easy you won’t believe it)

What a set of words this inverse Square Law, also known as inverse square law or inverse square law of distance, don’t you think?

Terrible, in fact I must admit that it is something that I avoided for a long time. It seemed horrible to me, how complicated, I’m not a nuclear physicist, why should I know it?

And so, enlightenment book or article where this awful term appeared, I discreetly skipped over inedible definitions like this:

The inverse square law, inverse quadratic law or inverse square law of distance, refers to some physical phenomena whose intensity is inversely proportional to the square of the distance to the center where they originate. In particular, it refers to wave phenomena (sound and light), and in general to central fields in three-dimensional Euclidean space, to electric fields and to non-particulate ionizing radiation.

Source: Wikipedia

But hey, I thought, I must not be the only one who is scared by this sum of words, so the time has come to know what the inverse square law is, don’t you think?

What is the inverse square law (for dummies ðŸ˜‰ )

The inverse square law helps us understand how the intensity of light behaves beyond what we mere mortals consider logical. I give you an example.

Imagine a scene where you have a photographer (you), a protagonist (in this case a cat), a distance between you and the cat (in this case one meter) and a light source (in this case a flash) .

So far everything is very normal, you measure the light, adjust the power of the flash, focus, press the shutter et voila, magic was done.

Now, imagine that you have two cats and you want to photograph them both, one in front of the other, let’s say you leave one where it is and the other you put it a little further back, to simplify let’s put it 2 meters from you. So:

Now comes the million dollar question. If cat 2 is twice as far from you as cat 1, how much light will reach it?

well here is the crux of the question. We mere mortals would say “half” (1/2) and perhaps adjust our exposure accordingly or even believe that we could save cat 2 by exposing for cat 1.

And three meters? Would you perhaps say 1/3 light?

Well no, wrong answers ðŸ˜‰ . The correct answer for 2 meters is 1/4 light, that is, only 25% of what the first cat will receive, and for 3 meters 1/9, that is, only 11% light.

Calculate the inverse square law

The inverse square law is calculated with the following formula:

Intensity= 1 / Distance2

So if I apply the formula, the first cat gets an intensity of 1/12 or 100%, but the second cat gets 1/22, which is the same as 1/4 or 25%. If it were 3 meters away, we would calculate 1/32: 1/9, which is the same as 11% and so on.

As you can see, the further away the light source is, the smaller the difference in intensity that objects receive.

Why is it important to know the inverse square law?

Knowing and calculating this law is essential in lighting, because as you can see in the previous calculations, there is a lot, a lot of difference between placing our subject at one distance or another with respect to the light source.

Based on this law we can deduce:

• That the greater the distance from the light source, the less intensity the object receives.
• That the loss of light intensity does not occur linearly, but rather decreases the square of the distance it travels with respect to the light source.
• Ultimately, and speaking clearly, we lose much more light intensity than we thought ;).
• That much more intensity is lost when we are relatively near the light source than when we are further apart.
• Therefore, it is not the same to move your subject 1 meter when we talk about it being located at an initial distance of 8 meters, for example, than to move it from 1 meter to 2 meters.
• In both cases we are talking about a single meter, but as you can see, the difference in light intensity in both cases would be very different.

If you work in a studio or want to do it at some point, this rule will be your day to day, but it also has its application for day to day, even if it’s hard to believe ;).

Uses and applications

As I have told you, in studio lighting it is essential to know this rule. It will help us know:

1. Where should we place the subject? depending on the intensity of the light that we want it to receive.
2. At what distance to place the subject with respect to the background. Do we want it to be illuminated or do we want a dark or black background?
3. If there are multiple elements in the scene, we’ll know what light intensity each will receive based on their distance from the light source. (For example, it can be very useful in group photographs).
4. The photographer does not live by artificial light alone, far from it. It will be useful for example “window” lighting.
5. To work with different light schemes.

Conclusions

Although to learn to apply the inverse square law You have to learn to use the formula that we have commented on previously (1/Distance squared), it can also help us in our day to day life without the need for mathematical calculations.

Because the inverse square law is the explanation of why it is so difficult for you to expose well for two subjects located relatively close, but not for those that are further away.

It’s also the trick you need to get black or completely white backgrounds. It is the gateway to understanding how light behaves, and thus lighting schemes and studio lighting.

I hope this article has been useful to you. My advice? Keep the information you need for the photographic level or the specific interests you have. At least it works for me ðŸ™‚