Inverse Square Again


I've written about the Inverse Square Law before. But I  wanted to give a little different perspective on the Inverse Square Law here by adding a crude little video I just created with an iPhone, a white board, an LED flashlight, and some sticky notes. Let's start out with a description from Wikipedia:


The first thing to keep in mind is that strictly speaking, the law applies to light emanating from a point source. Most any photographic light we might use is much larger than a point source, so exact meter readings aren't going to happen. Where the law says that if you double the distance between the light and the subject the light will be 1/4 power, in practice it will be brighter than you expect. So please don't run off and set up a softbox, umbrella, or octabank and measure with your meter and come back saying it doesn't work. Please refer to the Wikipedia section on photography for more info.

What is more important here is the concept. Know that the closer your light is to the subject the faster it will fall off. As you move the light away from your subject, the slower it falls off. In practical situations, move your light in close to your subject if you want the background to go dark. Move the light further away if you need to even out the light (for example you want to have the background lit up or you have a group of people who are not all on the same plane with the light source).

You can almost think of light fall off similarly to depth of field. When you are in close on your subject, with high magnification, the depth of field falls off quickly. Only a small part of the scene is in focus. With the light in close, just a small part of the scene is lit and the brightness falls of quickly. When you are further away from your subject the depth of field is greater. When the light is further away, the intensity is more constant/even through the frame.

I think there is still some confusion about why light falls off so quickly. What is happening is that as the light photos stream away from the light source, they spread out in a cone-shaped pattern. The light doesn't really get dimmer, but the photons have to spread out further to cover the area of the cone pattern as they move away from the source of the light. As they move away the rays start to get more parallel and at that point the falloff stops happening. To show that the light is not getting dimmer, think of a city skyline in the distance. You can see the lights in the windows of the buildings when you are miles away. But there isn't any chance that those lights are illuminating you when you are at a distance. Same thing with an airplane flying overhead at night. You can easily see the marker lights on the plane at their point of origin, but they are too spread out by the time they actually reach you to have any effect on lighting you.

Think of the sun and earth. If we were able to be close to the sun the light skimming across the planet would be much brighter on one side than the other. But due to the distance between the sun and earth the light rays from the sun are reaching us in a parallel fashion. The light on the top of a mountain is the same intensity as at the base of the mountain if there is nothing blocking the light and causing shadows. When you stand on a beach and look out to the horizon, the brightness remains constant. You can see a ship off on the horizon many miles away. It doesn't fade into darkness until the sun goes down. The same amount of light hits the sand where you are standing as hits the ship on the horizon.

Here is the video:


For this demo I've set up a small LED flashlight as the light source. It is not a point source, but I think it should do for the demonstration. 

At first I have it set at 6 inches from the whiteboard and I have drawn a circle around the light hitting the board. Next. I moved the light back to 12 inches and drew another circle. This should start making things click if they haven't already. Note that the light expanded in all directions when I moved it back.

Then I added another element--sticky notes. I have one here that is approximately the size of the original circle that I used to cover that inner circle. How many sheets of paper will we need to cover the larger circle caused by doubling the distance of the light to the white board? At first you may be tempted to answer TWO. Seems reasonable. Double the distance equals twice the size. But that is incorrect. The light beam is expanding in all directions, so to cover the second circle I needed 4 pieces of paper. The light has spread out so that is is 1/4 the intensity at twice the distance. If I doubled the distance again so the light was four times the distance, it would take 16 pieces of paper to cover the circle.

I hope that this gives a little clearer demonstration of what is happening to the light beam as it expands as it gets further and further away from its source.

Here are a few more links with photographic demonstrations… This Week in Photo; Mark Wallace's YouTube video; and WikiPedia.