Right. So everything I said in the last post with diagrams was wrong. Not that the math was wrong, but what it MEANT was not what I meant it to mean :loco::facesmack:. I'm one of those "don't look it up, work it out from scratch" kind of annoying mathematicians, but that way you can find new ways of looking at things. More often, you just rediscover the wheel.
I'm going to go back to the simpler case of uniform magnification on the focus plane and see what we get from there.
M
In imaging, magnification is usually linear magnification, the difference between object size and image size. This should not be confused with visual instruments like telescopes and microscopes, with describes angular magnification (also note, that definition is different between telescopes and microscopes (a telescope working at 1x is not the same as a microscope working at 1x). But the difference is practical. Linear magnification allows us to predict the image size of an object in an imaging system, where angular magnification allow us to predict how something will appear when we look at it.
And this is where linear magnification can give two perceptually different results. If you shoot at 1:1 (or at 1x) on a medium format camera and APS-C camera, the resulting image will appear that the APS-C has more "magnification" simply because it has a smaller sensor. A 1cm object will appear larger on a smaller sensor simply because 1cm is proportionally larger on the small sensor.
I am not sure this will be helpful, but although image and object planes are conjugate, they are not the same appearance and are not directly related to point spread. So an f/2 lens will have the same depth of focus, the focused light cone will intersect the image plane at the same angle regardless of focal length, but the displacement from the image plane will represent different object distances because of focal length--think how far long focal length on a view camera has to be moved to focus from infinity to 1m compared to wide angle illustrating the image-side point spread is not the same as the object-side point spread (although those can coincide as you are doing). DoF is describing the appearance of the object-side point spread.
So how does this impact the visual appearance of the OFF image? So as you know, the difficultly with equivalence is it is like Home Depot--it almost has what you want. So in equivalence you can get many, but not all variables to coincide. And the same thing seems to be happening here. So if you look at the specular highlight on the ruler two feet behind the lens, the out of focus image does not appear the same, even though the DoF is equal. I think it is related to relative size in relation to perspective, as I posted above--the difference in the sizes of two object in an image is proportional to their distances from the camera. So in this case, the 250 is further from the lens, but the ruler end is fixed at 2ft for both. So while the DoF is identical in each image, the linear perspective (at least in terms of identifiable points in the image) is different.
In short, you can make DoF coincide, but not linear perspective and hence magnification, at least for objects within the frame. This may be the reason we can perceive the same DoF, but not Bokeh.
Just a thought.