Originally posted by BigMackCam Many thanks, all, for the assistance. It's very much appreciated as always

Splendid. This is exactly what I need

I note the limitations of using "thin lens" approximation. For my application, absolute accuracy really doesn't matter.

I'd love to see the math, if you can spare the time and it won't run into pages. A formula or three I might be able to deal with... (famous last words

).

Thanks again!

LOL! OK! You asked for it! ...... Sticking to only three equations is tough, though......

For various reasons, the distances indicated on lens barrels are the total distances from the camera's focal plane to the subject. This probably makes sense for doing flash-distance calculations and for replicating tripod-to-subject setups. But it makes the math for changes in flange distance really messy -- the dreaded quadratic formula is involved!

The basic thin-lens formula for the camera-to-subject distance is:

C = F*(2 + m + 1/m)

where C is the camera-to-subject distance, F is the focal length of the lens, and m is the optical image magnification. If you know F and have C set to the MFD, then you can calculate the corresponding m. But it involves the quadratic formula. The value of m at the MFD is the one in the following quadratic equation:

0 = m^2 - (MFD/F - 2)*m + 1

I'm not going to turn the crank on that formula here because: 1) it's a mess and 2) it's often not right for non-thin lenses. For example, the quadratic formula blows up if you plug in the numbers for the Pentax 100mm f/2.8 Macro lens. For that lens, the quadratic equation solution involves imaginary numbers which must have something to do with those Pentax pixies!

Instead, it is better to estimate the maximum subject magnification at minimum focus distance by another means. Maximum subject magnification can be found either in the specs of the lens, on markings on the lens barrel, or by taking a picture of a ruler at the minimum focus distance (just remember to use the correct FF or APS-C frame size in estimating the magnification). Then you can use the fact that a flange displacement of d will change the magnification by exactly d/F. A wee bit 'o algebra with the thin lens equation can compute the new minimum focus distance, MFD', from the original MFD with an adjustment for flange offset, d, with focal length, f, at the max magnification, m:

MFD' = MFD - F*(1/m - 1/(m+d/F) - d/F)

Note that this calculation still has the thin-lens approximation in it but it should be fairly close if d is not too large.