Originally Posted by Bob Williams
The formulas you need are
1) 1/f = 1/a + 1/b
where a = subject distance, b = distance between the lens and the ccd, and f is the focal length of the lens. and
2) magnification = b / a
From these two formulas it is easy to derive the formula John gave you, and also easy to figure out your new mfd .
Your mfd comes from the fact that travel in your lens only allows it to get so far from the ccd (that is, b can only get so big), thus a can only get so small. Adding a 24mm extension tube essentially adds 24 to your maximum value of b, thus allowing a smaller minimum value for a, thus increasing magnification.
Example: a 100mm macro lens has a maximum magnification of 1. This means that when focusing as close as possible, b / a = 1, so b = a. Thus formula one gives
1 / 100 = 1 / a + 1 / a, so 1/100 = 2/a or a = 200. The mimimum focus distance is 200mm, and when at this mfd, the lens is 200mm from the ccd.
Now imagine adding a 100mm extension tube. Then the furthest we can get the lens from the ccd is b = 300, (we used to be able to get 200mm from the ccd, but we've added 100mm) and we can compute the new a using formula 1), as follows:
1 / 100 = 1 / a + 1 / 300
This gives a = 150mm for our new mfd. (And, of course, our new magnification is 300 / 150 = 2, just as predicted by John's formula).
Having said all of this, it the formula does not really work for some lenses in real life, for two reasons. The first is that focal lengths of some lenses change as they get close to the subject (so the approximation gets worse as you get closer). I guess for your 500mm, the formula will be pretty close, though.
The other problem is that a is the distance of *something* to the subject, but it might not be the front element of the lens. Thus what you really have to do is compute mfd with and without the extension tube, and subtract the difference from your old mfd to get your new mfd.
I hope this helps...
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