Inverse Square

You have heard, perhaps, of the Inverse Square Law. I hope you have. Because it is rather important in photography.

The Inverse Square Law says that the intensity of light shining on an object from a light source decreases with the square of the distance of the light source to that object.

You can see what this means for us in practice: dark backgrounds if we aim a light forward from where we are (say, a pop-up flash). If the background is ten times farther away than your subject, it gets 100 times less light. Solution: do not have the light where your camera is. Or bounce. Or use several flashes. Or use ambient light also (“dragging the shutter”).

Important note: It is important to realize that this applies to the distance between light emitter and subject. Not the distance between you and the subject!  (If you find this hard to visualize, consider this: when you back away while looking at a Caucasian, he or she becomes a smaller Caucasian to you, not an African-American).

Other than dark backgrounds, what else does the inverse square law mean to you in practice? This, for instance:

  • If you move a studio light twice as far from a subject, you lose two stops of light (2 squared = 4, and two stops equals a factor of four).
  • If you move it 41% farther, you lose just one stop, since 1.41 is the square root of 2.
  • To get one stop more light, move the light closer by 30%, to 70% of its previous distance, since 0.707 is the square root of 0.5).

So knowing a little math, geometry and physics comes in handy. I speak not as an engineer, but as a photographer. I can move a studio light into the right position to get a  stop more, or a stop less, light without metering.

And now, so can you. You are welcome.


2 thoughts on “Inverse Square

  1. This is even more important underwater where the medium(water) is 800x more dense than air, so the inverse rule diminishes light by a greater factor-penetration of light is limited to 10-12 feet which means any light source stronger to get greater penetration is harmful to marine life,and particles in the water become visible also on the results. but the inverse law is really evident underwater.

  2. So, if you have a pop-up flash and stand 10 feet from your subject, then move back to 14 feet, you loose one stop of flash reaching your subject. If you moved further back to 20 feet from your subject you would loose a second stop reaching your subject. If you then moved forward 30% of 20 feet, or 6 feet, you would be back at 14 feet from your subject and would gain a stop.

    If you are in a studio, camera to subject distance remains constant and the lights are moved independently. If light from source to subject dissipates following inverse square, what happens to light reflected by your subject? Does distance affect light reaching the lens?

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