The response to Lee's post is a little heavy on the math side and possibly completely off topic for the original question. What I would like to do here is provide an explanation for analog photographers how circles of confusion behave for different media, focal lengths and distance ranges, how they affect DOF and far distance blur. If folks deem this as too off topic for this thread, please move it to some more suitable forum or make an article out of it. If you don't want to read through this whole mess, scroll al the way down for the most relevant conclusions.

I would like to start my explanation with the equation published in the highly relevant wikipedia article: c = m*A*|S2-S1|/S2.

c .... diameter of the circle of confusion in the film plane
m ... magnification: size of the image of the subject in focus divided by its real size
A ... diameter of the aperture (not the aperture number !! )
S2 ... distance of a point which is out of focus and creates a circle of confusion with diameter c
S1 ... distance the lens is focussed on. Points at this distance are projected into the film plane as sharp points.

Let's analyze this equation: for a given focal length and aperture, and a given distance S1 we can calculate m, and from there create a function c(S2), which shows how the COC diameter changes with distance. Around S1 the COC diameter rises linearly with S2, but as S2 moves further and further away towards infinity, c(S2) starts to saturate, i.e. it converges towards a maximum. Infinite points are not infinitely blurry!

How does DOF come into this? We can establish a depth of focus by (arbitrarily) setting a limit for c, the diameter of the COC. Note, that the subject doesn't abruptly switch from tack sharp to blurry, but that the blur increases gradually as a point moves further and further out of focus. This means that DOF describes only one characteristic number of the whole COC behavior. Setups with the same DOF can have totally different behavior at different distances from the focus point!

One more important implication from the original equation: (S2-S1)/S2 saturates if S2 goes towards infinity. If m is very small (i.e. large focus distance S1, short focal length), c may never reach its limit set for the COC, even if S2 goes towards infinity! This is the range photographers call the hyperfocal range. Again, this hyperfocal range is nothing which abruptly appears. As m gets smaller and smaller, the c_max gets smaller and smaller.

Let's back this up with a few examples (all distances in meters unless noted otherwise):
1. 50mm F/2.8 lens focussed at a distance of S1 = 2
m = f/S1 = 25e-3
A = f/2.8 = 17.9e-3
c = 446e-6 * |S2-S1|/S2

2. 300mm F/2.8 focussed at a distance of S1 = 12
m = f/S1 = 25e-3
A = f/2.8 = 107e-3
c = 2679e-6 * |S2-S1|/S2

If we compare these two results, we see: while the proportional factor is larger for the 300mm lens, so is S1. For small c limits, these two effects cancel each other and we get the same DOF. Still: if S2 goes towards infinity, the term |S2-S1|/S2 converges towards 1. This means, that the 300mm lens blurs inifinite points much more than the 50mm lens does!

So what happens, if we increase S1 tenfold, like Lee has done in his example?

The magnification goes down by a factor of 10, so we get a c50 = 44.6e-6*|S2-S1|/S2 and a c300 = 267.9e-6*|S2-S1|/S2. Since Lee imposed a c_max of 30e-6, the term |S2-S1|/S2 must get rather close to 1 for c50 to reach this value. But since |S2-S1|/S2 saturates at one, we need much larger S2 to reach c50 = 30e-6 ! We are deep in the hyperfocal range! The proportioality constant for c300, however, is still much larger than the 30Ám limit, so |S2-S1|/S2 can stay well below 1 where it behaves like a linear function. In Lee's example the 50mm lens is in the hyperfocal range, but the 300mm lens is not.


Until now we have only changed the focal length and focus distance, but how does film format size matter? Again, the equation from wikipedia answers this question completely:

If the film format increases by factor n, the magnification m must increase by the same amount n to maintain the subject frame. So if we adjust the focal length of the lens to the film format (e.g. use 110mm lens for RZ67 instead of 50mm for EOS 3), we keep S1 the same. If we also keep the aperture diameter A the same, we get increased COC diameter, again, by factor n.

It is now up to the photographer whether he/she accepts a larger c for the larger film frame. If we want to produce the same print, c may become larger for the larger film size, since we need to enlarge less. If the whole point of the larger film frame is increased image detail, we would not accept larger c just because of the larger film frame. If the film frame gets way larger, e.g. 4x5" instead of 35mm, the LF lenses may not be as sharp as the 35mm lenses, so we may accept a somewhat larger COC limit, but not by the whole frame size quotient. It's these considerations which make comparisons between frame size so subjective!

If we accept an increase in c_max by the factor n, nothing changes for DOF. The 110mm F/2.8 lens for my RZ67 does roughly the same as a 50mm F/1,4 lens would do on my EOS3, since they produce roughly the same view angle at the same distance and they also have the same aperture diameter. Note, that technically 110/50 is slightly larger than 2.8/1.4, so the RZ67 should have slightly less DOF at comparable framing. Since, as mentioned before, out of focus blur does not happen abruptly but comes in gradually, it is very difficult to see small DOF changes in a real image. Therefore I would consider the before mentioned RZ and EOS setup sufficiently close to be equivalent.

If I want to take full advantage of the additional resolution the RZ67 affords me, I must not increase the c_max limit for the larger frame. In this case I need to stop down the RZ lens even more, towards F/5.6 in order to stay within my self imposed COC limits!

I hope this explanation has helped clarify the whole DOF/COC topic for all those who made it through my post.

Here are the essential results:
1. At the same short distance, and with the same aperture number (e.g. F/5.6) you get same DOF regardless of focal length.
2. The back ground blur depends mostly on m*A, which means the closer your main subject is and the larger your aperture diameter, the more blurred the far away back ground gets. This means, that it's much easier to get dreamy back ground blur with a long focal length lens! Similarly, even with a large aperture number, a wide angle lens will not blur the back ground too much.
3. In order to guestimate the back ground blur one can think of the aperture disk placed at the main subject. The aperture disk will appear as large in the film plane as infinite points will be blurred.
4. At some distance, the back ground blur will be too small to look blurry. Shorter focal length lenses do this at shorter distances than tele lenses. This distance is called the hyperfocal distance.