Yes, I think I demonstrated that DOF is dependent on magnification in a specific way, i.e. inversely proportional to M squared. Since M is directly proportional to focal length, DOF is also inversely proportional to f squared. That is all I stated in my original post. These relations apply only in the range where M << 1 and the subject distance is much less than the hyperfocal distance for the lens and aperture combination. These limits, however, cover most non-macro use of telephoto lenses. For example, with the 105 mm f/2.8 lens settings in my test, I calculate a hyperfocal distance of about 242 m (assuming a circle of confusion of 16 microns that is often considered appropriate for the DX sensor size). When subject distance is a significant fraction of the hyperfocal distance back DOF begins to increase hyperbolicly, so these approximations no longer apply.
Your comment about post-recording magnification is very relevant to this discussion. Assuming you want to reproduce the same field in the final print by cropping instead of using the TC, you would need to use a smaller circle of confusion to compensate for the increased enlargement factor in order to see equivalent out of focus blur and apparent DOF. Since this increase in enlargement factor is identical to the TC focal length factor, and since DOF depends directly on COC as well as f-number, you now have two factors to cancel with the M (or f) squared in the denominator, and perceived DOF is theoretically identical. In other words, perceived DOF is dependent on the total "magnification" including image magnification and later enlargement factor (as well as viewing distance). I did this often in the mid-1960's when my only lenses for a Konica SLR were a 52 mm and 135 mm; I did my "zooming" with the enlarger, sacrificing increased grain and some sharpness degradation to get the framing I wanted without the ideal focal length lens.
I chose my test conditions above to illustrate DOF dependence in a small image, suitable for posting. I also took a couple of shots at twice the distance, but would have needed a much larger image to illustrate them due to the greater DOF, and the results were similar. Any larger subject distances would not fit in my basement, and it was snowing here yesterday. :wink:
My TC-17EII does not work with my other lenses (I once had a TC-14A, but maybe I lent it to a friend, or lost it. While my lens collection is tiny compared to yours, I suspect this may be a case similar to your 45 mm f/2.8 experience!). A similar test could be done using two lenses of different focal length. Maybe in the Spring, when it gets warm enough here to set up a controlled test outside, I can continue.
I also rarely get upset about making mistakes, as long as I can eventually correct them; they are an essential part of the learning process, and we are all subject to human frailties. As a scientist (in real life) and as a photographer I often depend on intuition, and sometimes it fails me. Thankfully, I have caught most of my professional blunders long before I published them. Having been involved in many animated technical discussions with colleagues, I understand well the difference between arguing about ideas, versus the personality conflicts that seem to occur regularly in this type of discussion on other boards. Often differences in opinion are due to unstated assumptions that affect the comparison. That is why I have tried to be as explicit as possible in explaining my reasoning, and I fear that I ended up being long-winded.
Although I spent a quiet New Years Eve at home with my wife and son, I did have a few glasses of wine, and stayed up much later than usual--my head is not aching, but it does seem a little harder to get the old body started this morning. :smile:
By the way, I always enjoy your artistic contributions to the Cafe, as well as, your equipment discussions and more technical explanations, even when I have a small disagreement with them. :smile: