macro - How can I calculate what the effect of an extension tube will be?

There must be a mathematical description of the difference that an extension tube makes to a lens -- is it something that can be easily described?

(For example, with teleconverters you can say things like "a 2x teleconverter will turn a Y-mm lens into a 2Y-mm lens, and will lose you 2 stops." Is there something similar for extension tubes?)

If there's nothing much you can say about magnification, in general, what about the change in closest focal distance? Is that also lens-dependent?

What about if we factor out the lens: is there any general way to compare the effects of (say) a 12mm and a 24mm extension tube on the same lens?

Answer

I do believe there are some formulas you can use. To Matt Grum's point, I have not tested these with zoom lenses, and to my current knowledge, they apply only to prime (fixed focal length) lenses. You did not specifically specify zoom lenses, so...

The simplest way to calculate the magnification of a lens is via the following formula:

  Magnification = TotalExtension / FocalLength
  M = TE / F

To calculate the magnification with an extension tube, you need to know the total extension...that is, the extension provided by the lens itself, as well as that provided by the extension tube. Most lens statistics these days include the intrinsic magnification. If we take Canon's 50mm f/1.8 lens, the intrinsic magnification is 0.15x. We can solve for the lenses built in extension like so:

   0.15 = TE / 50
   TE = 50 * 0.15
   TE = 7.5mm

The magnification with additional extension can now be computed as follows:

  Magnification = (IntrinsicExtension + TubeExtension) / FocalLength
  M = IE + TE / F

If we assume 25mm of additional extension via an extension tube:

  M = 7.5mm + 25mm / 50mm

  M = 32.5mm / 50mm
  M = 0.65x

A fairly simple formula that allows us to calculate magnification fairly easily, assuming you know the intrinsic magnification of the lens (or its intrinsic extension.) If we assume the wonderful 50mm lens is the lens you are extending, to create a 1:1 macro magnification, you would need 50mm worth of extension. The problem here is that if you add too much extension, the plane of the world that is in focus (the virtual image) might just end up inside the lens itself. Additionally, this assumes a "simple" lens, one with very well-defined and well-known characteristics (i.e. a simple single-element lens.)

In a real-world scenario, having a clear understanding of any particular lenses characteristics is unlikely. With lenses that focus internally, or zoom lenses, the simple formula above is insufficient to allow you to calculate exactly what your minimum focusing distance and magnification can be for any given lens, focal length, and extension. There are too many variables, most of which are likely to be unknown, to calculate a meaningful value.

Here are some resources that I have found that provide some useful information that might help in your endeavor: