Originally posted by GUB I don't think so. An analogy I use to think this out is visualizing a pair of chopsticks held between thumb and forefinger. Insert another finger at the other end and draw it towards your other fingers.The base is the lens, the tips of the sticks are points on the horizon and your finger is her head - this is pretty well how perspective works and you can soon see it is not a lineal relationship.
Basic formula:
object size on sensor = (focal length) * (object size) / (object distance)
For the mountains in the background, lets say 1000 metres away. Change the focal length from 35 to 70mm and readjust your position to keep the model the same size. You've now changed (object distance) of the mountains from 1000 m to 1003 m. Moving a few feet to keep the model the same size does essentially nothing to your distance to the mountains, but you've doubled the focal length so you've doubled their size on the sensor (or very very nearly doubled the size).
This won't be close to a nice linear relationship if the background and subject are close to the same distance from you.
---------- Post added 09-11-17 at 09:18 PM ----------
Originally posted by GUB Yes but if the two shots were done by the same lens the cropped one has to be the one with the least horizon (and the one that he has stepped back with). And this should be the one to have the smaller head to horizon ratio which it isn't..
The second part doesn't follow. This head to horizon ratio is independent of any cropping, and (assuming the same focal length) is solely on the photographer's position relative to the girl.
Assuming the same lens-
1) Model is slightly smaller in the OP's image, so the photographer is back a bit compared to "3897".
2) The background covers more of the horizon in the OP's image... he cropped 3897 slightly more horizontally. The difference here is very small.
3) The absolute blur on the background of 3897 is a little bit greater... it should be as he's closer to the model and hence focusing closer so the background gets blurrier. Possibly having stopped down a bit in the first image would also contribute.
4) The ratio of the models head size to a pair of mountain peaks is higher for image 3897.
I see nothing inconsistent with the above.