... or you do macro or close-up photography using a macro tube on a 400 mm lens.[a href=\"index.php?act=findpost&pid=187782\"][{POST_SNAPBACK}][/a]
Umm ... using a 400 mm lens on a 35-mm-format or APS-C-format camera at close distance is one of those situations where the 2nd-order effects mentioned above hardly show up. Here, Michael's statement would be true; when keeping the magnification constant then it doesn't matter whether you were using a 200 mm lens or a 400 mm lens, the resulting DOF would be the same.
It's obvious that a 200 mm lens gives you a much shorter DoF.[a href=\"index.php?act=findpost&pid=187782\"][{POST_SNAPBACK}][/a]
Huh!? Shorter than what? Than the 400 mm lens? Definitely not.
Everybody knows the three basic rules of depth-of-field, or DOF for short (on constant image format):
1. DOF is wider at smaller aperture; DOF is narrower at wider aperture.
2. DOF is wider with shorter focal length; DOF is narrower with longer focal length.
3. DOF is wider at longer focusing distance; DOF is narrower at shorter focusing distance.
When we eliminate the effect of rule 1 by keeping the aperture always the same and compensate for a longer focal length with a longer distance in order to keep the magnification of the main subject the same then rules 2 and 3 will cancel each other out. When using a longer lens then you'll have to back up in order to keep the magnification the same. The longer focal length will reduce DOF, and at the same time the longer focusing distance will increase DOF. These two effects annihilate each other, and they do so not approximately but exactly---in a first-order approach.
This is what Michael's essay is about, and it's nothing new. It has been a well-known fact for ages. Actually, we can boil the three rules of DOF down to two rules:
1. [Same as rule 1 above]
2. DOF is wider at smaller magnification; DOF is narrower at larger magnification.
Focal length and focusing distance per se don't matter; it's the combination of the two, i. e. the magnification, that matters---in our first-order approach.
If we'd stop here then we're in perfect accordance with Michael's essay. Unfortunately we just can't stop here. Second-order effects raise their ugly head, and they will affect DOF to a degree that is not just academic but makes a real difference in many (not all) real-life situations.
The 2nd-order effect I am talking about is the fact that across the depth of the field, magnification is not constant. For close objects it's larger than for distant objects ... that's a very trivial fact of life. So when trying to compensate for a longer focal length through backing-up then you can achieve the same magnification as before only for one single distance. You'd back up so the main subject will appear at the distance presicely corresponding to the increased focal length, yielding the same magnification as before. However, now objects before and behind the plane of focus will appear at different magnifications as before---that is what we call perspective, and it also affects actual DOF. With the longer focal length, background objects appear larger than with the shorter focal length at shorter distance, and so, according to rule 2 in the modified set of DOF rules above, background DOF becomes narrower (and foreground DOF becomes wider (!) but the gain in the foreground is less than the loss in the background).
And that's not just academic nitpicking; it often (not always) will make a visible difference ... as Doug's examples easily show. It tends not to make a significant difference only when the background is at infinity or when DOF is very small in relation to the focusing distance (i. e. with very long lenses or at close-up range).
There are finer points that also can affect actual DOF, like focusing methods, the physical length of the lens, the ratio of exit to entry pupils, residual lens aberrations, diffraction, and others. Michael called them 2nd-order effects that should be neglected. In fact those are not 2nd but 3rd and 4th and higher-order effects ... and yes, for most practical intents and purposes those can be neglected indeed. The 2nd-order effect described above, however, mustn't be neglected generally.
-- Olaf