Lens to subject distance formulae for known magnification factor and fl?

[Bill Glickman]

What is the formulae to determine the distance the subject will be from the lens with a known magnification factor. For example, if I shot an apple on 8x10 and wanted to fill the format, say 3x magnification, what would the distance from t he apple to the lens be using a 210mm fl macro lens. I guess it does not matter if the lens is macro or normal, fl is fl, right? Thank you...

[Michael S. Briggs]

Define d_s = distance to subject, d_f distance to film, m the magnification and f the lens focal length. Be sure to use the same units for all the distances, e.g., mm. The basic equations are:

1/d_s + 1/d_f = 1/f and m = 1 / ((d_s/f) - 1) = (d_f / f) - 1

For your question one uses the last equation, rewritten as:

d_s = f (1/m + 1).

For f = 210 mm and m = 3, this gives d_s = 280 mm.

Properly, these distances are measured from the principal planes of the lens. For lenses other than true telephotos, measuring from the position of the aperture diaphragm should be sufficiently accurate.