Now I've got this in my head. Jim has the log relationships right on.
However, what we are dealing with here is light ratios and not changes in f-stops. Light ratios describe the intensity of one light in relationship to another and the ratio of change in intensity when a single light is moved either closer or farther away from the subject.
This ratio is described mathematically by the Inverse Square Law. This "law states that the intensity of light on a surface is inversely proportional to the square of the distance from the light source." (Adams, The Negative, p. 158)
It works like this. If you halve the distance, the light intensity increases by four. If you double the distance it falls off by 1/4. In either case the change is 400% or 1:4.
Thus, if you have two lights of equal intensity lighting a subject with one light 4 (4x4=16) feet away and the other 8 (8x8=64) feet the ratio is 1:4 (or 4:1) (64/16=4).
Now to the original example with a ratio of 1:3 instead. Keeping the closer light at 4 feet, the farther light would then be about 6.93 feet away and represent roughly 1 2/3 stops (6.93/4=1.7325) less light than the first.
How's that for someone who nearly gets a aneurysm doing simply math?
Peace! Sidney
