Inverse Square Law In Digital Photography

Today blog seems like a math or physics article but please read until the end of the blog and I promise that it would be interesting once you find its connection with photography. It’s practically very important if you are dealing with lots of flash lights or studio strobe. So, without wasting any time, let’s get into it and see how can we apply it to our photography world. In physics, an Inverse Square Law is defined as "any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity".  And mathematically, we can written this law as,

Intensity=1/d2, where d is the distance between light source and object.

Inverse Square Law

Inverse Square Law

If you read above definition correctly, it mentioned “any physical quantity or strength”. That means anything on this earth can be related with this law (for e.g. force, energy, light etc). But today we are going to relate it with photography and that means we will talk about lights and its relation with distance according to inverse square law. We already saw mathematical definition of this law which looks pretty confusing especially if you don’t like math. Let me put it as simple as possible in plain English. We get brighter light when we are close to the light source and light gets darker and darker as we increase the distance from light source. I am sure you will agree with me on this and it sounds very obvious too right?

Now let’s follow above inverse square law formula and put this definition in other way. An object that is two times far from the light source will receive a quarter of the illumination. In photography world, this means, if you move your subject from 1 feet to 2 feet away (double the distance) from the light source, you will need four times as much light to get the same exposure. It’s because according to Inverse Square Law, light intensity at the 2 feet distance will be 1/22 which is 1/4. This extra light can be achieved by changing either Aperture or Shutter speed or ISO value by two full stops to compensate the exposure. If you change aperture, you need to wide open the lens by two full stops and if you plan to change Shutter speed, you need to decrease shutter speed by two full stops to allow enough ambient light to get the proper exposure. Similarly, you can also change ISO value by two full stops to get the same exposure.

This light fall-off behavior is pretty interesting if you do more research. As you move the subject far and far from light source, light fall-off is not that much significant as it is in the beginning. Let’s say you get 100% light in 1 feet distance from the light source, we can form following table to analyze behavior of light with the distance.

Distance

1

2

3

4

5

6

7

8

9

10

Intensity of Light

1   (100%)

1/4 (25%)

1/9 (11%)

1/16 (6%)

1/25 (4%)

1/36 (3%)

1/49 (2%)

1/64 (2%)

1/81 (1%)

1/100 (1%)

So when you move your subject from 1 feet to 2 feet from light source, light intensity was decreased by 75% but when you move further from 2 feet to 3 feet and 3 feet to 4 feet and so on, light fall off is very minimal and at the end there is no difference. That means distance plays great role with behavior of light. This may help you a lot and save your time when you are dealing with lights and get results you never expected.