The idea: vergence changes as light travels
A +10.00 D lens focuses parallel light 100 mm behind itself. Twelve millimeters downstream, at the cornea, that light has only 88 mm left to travel, and vergence is the reciprocal of the remaining distance: 1 / 0.088 m = +11.36 D. The eye experiences +11.36 D, not +10.00 D. That is the whole phenomenon; the formula just automates the reciprocal.
The formula and its sign convention
F' = F / (1 - d x F), with d = (old vertex - new vertex) in meters, positive when the lens moves closer to the eye. Both canonical directions:
- +10.00 D at 12 mm to the corneal plane: d = 0.012, F' = 10 / (1 - 0.012 x 10) = 10 / 0.88 = +11.36 D.
- -10.00 D at 12 mm to the corneal plane: d = 0.012, F' = -10 / (1 - 0.012 x (-10)) = -10 / 1.12 = -8.93 D.
Plus powers grow as the lens approaches the eye; minus powers shrink in magnitude. Going the other way, cornea out to a spectacle plane, d turns negative and the effects reverse.
When it matters
The common rule of thumb is about 4.00 D and above, where an ordinary fitting difference moves the effective power by an eighth diopter or more. Contact lens conversions from high-power spectacles always compensate. Near the extreme, when 1 - d x F approaches zero, the formula blows up; the calculator flags that region as outside the practical range rather than printing a meaningless number.
Work examples on the vertex calculator, and see the vertex distance reference for typical fitting values.