Photography and light: The inverse square law

With respect to light, the inverse square law states that:
“the intensity of light radiating from a point source is inversely proportional to the square of the distance from the source”.

This means that a subject 1 meter away from a light source would be illuminated 4 times more than a subject 2 meters away from the same light source:

• 1/(1*1)=1
• 1/(2*2)=1/4

So if you were to move a correctly exposed subject 1 meter away from your light twice the distance, it will receive 1/4 times the light, and in turn would be 2 stops under exposed.

If you were to move a correctly exposed subject 2 meters away from you light half the distance, it will receive 4 times more light, and in turn would be 2 stops over exposed.

Based on this, if the subject was close to the light source its illumination would vary more widely if it was moved a little bit closer or further away from the light. Whereas if the subject was far from the light source, its illumination would vary slightly if it was moved a little closer or further away from its current position. That is because, as the distance becomes longer and longer, the difference between its squared inverse becomes smaller and smaller:

• A subject one meter away from a light source would receive 1/4 the light if moved 1 meter away.
  1/(1*1)=1, whereas 1/(2*2)=1/4
• A subject 9 meters away from a light source would receive roughly as much light if moved 1 meter away.
  1(9*9)=1/81, where as 1(10*10)=1/100

Putting the inverse square law into practice

Let’s say you’re shooting a model against a backdrop. You want the model to be correctly illuminated while the background dark. You place the model away from the background and close to the light source.

If you want the model and the background both bright and well illuminated, you place both of them close to each other but far away from the light source.

If you’re shooting a group of people, and they are all close to the light source. The one closest to the light would be significantly more illuminated than the one furthest away in the group. However, if you place all people far away from the light source, they will be roughly equally illuminated from the closest to the furthest.