The Inverse-square Law and the Decay of Light
This article will start with explaining the Inverse-square Law in the simpliest terms possible without getting too technical, then it will use the Inverse-square Law formula on some real-world examples.
How Light Intensity Declines with Distance
Light intensity declines greatly as the distance it must travel increases. This is due to the fact that light spreads out as it travels. But pertaining to photography, light intensity is relative to the distance it is from its subject. Understand that the closer a light source (like a flash) is to the subject then the more uneven the light will illuminate. The farther away a light source is then the more even the illumination of the subject will be but the light source will, of course, weaken. This often means the best light is one that is very strong and very far from the subject, such as the sun. Note: special effects can be had with light sources very close to the subject.
The Formula of the Inverse-square Law
The inverse-square law refers to the inverse (dividing something into the number one) of the distance of the subject from the light source multiplied by itself (squared). This gives the light's intensity.
The formula is simply written like this:
* "∝" means "is proportional to"
Large Amount of Light Decay
The wall is approximately 11.5 inches (29 cm.) wide. Use the Inverse-square Law formula from above to check the light intensity as it travels across the wall. At 1 inch distance from the flash the intensity is 1. At the middle of the wall (6.75 inches from the flash), the intensity is 0.02 — a huge difference in only 5.75 inches! And at the end of the wall (12.5 inches), the light intensity is only 0.006! This means the light changes 0.994 in intensity from one side to the other.
Small Amount of Light Decay
The wall is still approximately 11.5 inches (29 cm.) wide. Use the Inverse-square Law formula to check the light intensity as it travels across the second wall. At 26 inches distance from the flash the intensity is 0.0015. At the middle of the wall (31.75 inches from the flash), the intensity is 0.001 — not a huge difference which explains the relatively uniform lighting. At the end of the wall (37.5 inches), the light intensity is 0.0007, which can be seen in the image; the left side is only a little darker than the right side. This means the light only changes 0.0008 in intensity from one side to the other.