For chiaroscuro shots like this, of a Sheridan student Monday night, I prefer manual flash power settings to TTL (automatic flash metering).

(1/125 sec at f/10, ISO 200.)

Why? Because TTL may try to average this and will therefore overexpose the bright areas. If I do it manually, once it is set correctly, it is set correctly, period.

Unless, that is, I change the distance between light source and object that is being lit. Closer gives me this:

And farther gives me this:

That’s because of the Inverse Square Law. The brightness decreases with the square of the distance. Twice as far means 4x less light. 3x farther means 9x less light (since 3×3=9).

And

• 1.4 times farther means 2x less light, i.e. one stop less, since 1.41 (the square root of two) times 1.41 is 2.
• 0.7 times closer means 2x more light, i.e. one stop more, since 0.7 (1 divided by the square root of two) times 0.7 is 1/2.

So—and remember this: every time I want one stop more light, I move a flash 30% closer (to 0.7x the original distance); and every time I want a stop less light, I move the flash 40% farther (to 1.4x the original distance).

See? Math can be useful! Who’d have thunk.