When a lens is moved away from the normal location determined by its direct attachment to a camera body, as in close-up macro photography, the effective aperture is no longer that marked on the lens barrel. This is caused by the increased distance of the nodal point of the lens from the plane of the film or sensor, and the effective aperture changes in accordance with the inverse square law. The required increase in exposure may be calculated by dividing the sum of the focal length of the lens and the length of the extension by the focal length of the lens, and then squaring the result.
In the formula F = [(FLL + EXL) / FLL] 2 , F is the factor by which exposure must be increased, FLL is the focal length of the lens in millimetres, and EXL is the length of the extension in millimetres.
For example, when a 50mm lens is used with an extension of 100mm, the calculation is:
F = [(50 + 100) / 50] 2, which simplifies to F = [150 / 50] 2 and hence F = 3 2 = 9.
The exposure must therefore be increased by a factor of 9x.