(01-29-2020, 01:50 PM)Mistral75 Wrote: Considering a complex optical system with several lens elements moving independently one from another, there is no direct relation between minimum focusing distance, maximum magnification and focal length. Other parameters have to be considered.
Anyway, most people speaking of variation in the angle of view, and not in focal length, when they talk about focus breathing, one can simplify things and consider each of the two lenses as if it were made of one single lens element. In this case, there is a direct relation between minimum focusing distance (MFD), maximum magnification (MM) and focal length at minimum focusing fistance ([email protected]):
[email protected] = MFD x MM.
HD Pentax-D FA 70-210 mm f/4 ED SDM WR: MFD = 0.95m MM = 0.32x ==> [email protected] = 304mm. The angle of view decreases with the focusing distance.
HD Pentax-D FA★ 70-200mm f/2.8 ED DC AW: MFD = 1.2m MM = 0.13x ==> [email protected] = 156mm. The angle of view increases when the focusing distance decreases.
Even if you "consider" the lenses to be single element lenses, your calculation is not correct. If you have a single element 200mm lens, the FOV will narrow moving focus closer to the lens. The reason is that you are not looking at the projected FOV from the focal point, but from a certain distance from the focal point ( where the image is actually projected). The formula you use is incorrect to try and calculate focal length.
In short: when the focal length remains the same, the closer you focus, the more narrow the FOV becomes.
Because the distance of the lens to the imaging plane increases, while focal length remains the same (so the FOV that gets captured decreases). My estimate of under 110mm at MFD is much closer than what the faulty formula you use gives.