Yes, that's a little weird. The thing in question is equalizing direct eye magnification and through-the-EVF magnification, and should not be influenced at all by aspect ratio.
The question is: how much magnification is required in the viewfinder to see the image at life-size?
In other words, how much magnification is needed to see the image with the same angle of view as the camera captured. A wide-angle image needs to be magnified more that a telephoto image because it needs to fill a larger angle of view than a telephoto image (which captures only a narrow angle of view).
Take the particular example of an optical viewfinder in an SLR or DSLR in which the image is 36 x 24mm on the ground glass. If you view it from 250mm away with the naked eye, you see the image at life-size if it was taken with a 250mm lens. If you want to see it at life-size when the taking lens is 50mm, then you need to use a magnifier lens in the viewfinder that magnifies 5 times, i.e. creates the appearance that you are looking at a 180 x 120mm image from 250mm away. The latter image fills a much larger angle of view than the former.
If you wanted to see a life-size image from a 25mm lens, the viewfinder must magnify the image by 10 times and the image will occupy an even larger angle of view.
Sorry Tom, but that is not the question I was asking. Your post above did answer the question quoted, but my question was the semantics of your statement regarding a "wider angle of view", which has nothing to do with seeing images at lfesize, but all about the wording.
To me, I look through a viewfinder. If I want to see a wider angle of view (i.e. more of the scenery in front of me), I need to zoom out - in other words, less magnification. If I want to see less of the scenery, then I need to zoom in - so more magnification.
So, TO ME, the statement "a wider angle of view" has nothing to do with seeing an image at life size, but purely about how much of the view in front of you appears in the viewfinder.
We have been talking at cross purposes. You are talking about the angle of view seen by the camera lens - how much of the view in front of you it captures in the image.
I was talking about a completely different angle of view, that seen by the person viewing the image, ignoring the content of the image. Imagine that you are looking at a pure white image that doesn't represent anything. It still makes sense to talk about the angle of view with which a viewer sees that image. Suppose that the image is 36x24mm. If you view it from 25cm (10") away, you see it with a very small angle of view. If you enlarge the image ten times to 360x240mm and view it from 25cm, you see it with a much larger angle of view.
I am distinguishing the angle of view seen when viewing the image in the viewfinder (even when looking at a blank image) from the angle of view seen by the camera lens and captured in the image.
The image appears life-size when the angle of view seen by the viewer equals the angle of view seen by the camera. In other words, it appears life-size when the viewing angle of view equals the taking angle of view.
Human eyes are of the internal focus type, i.e. their physical FL changes when focusing between near and far objects.
A photo can't do that, it always has the fixed FL from the moment the shot was taken.
Human perception is much more complicated than what the camera sees.
It depends on how good your eyesight is. My eyes are far from perfect and I find it quite difficult to accurately compare the image I see in one eye with that in the other. I think I would have found it much easier when I was younger and my eyesight was better.
Canon R5 FF camera in full sensor mode: EXIF reports 62mm from my RF24-240 when my two eyes experience the same magnification with my personal diopter adjustment.
The easiest way for me was to rotate the camera counterclockwise to portrait orientation (EVF on the left of the camera) and put the EVF up to my right eye, and then choose a target that has clear repeating horizontal lines.
I am not at all sure why you are talking about angle of view. What does angle of view have directly to do with angular subject magnification?
You could conceivably use AOV in some intermediate math as long as you adjust for other factors,, but the fact is, you can have the same subject magnification with different angles of view. If my FF camera did crop mode by matting 61% of the sensor area instead of magnifying an extra 1.6x, the angle of view would be different, when the magnification would be the same. The optics of the viewfinder also play a role; the same angle of view with a sensor size and focal length
We have an angle of view windowed in the used sensor area (based on focal length and sensor size), and we also have an angle that the EVF appears to exist at (independent of focal length), but neither defines magnification alone without other factors.
That's how I understand "Angle of View". Tom seems to be conflating that with how large an EVF or ground glass screen appears to be as an angle, which should have another name, like "Angle of Display".
If we could digitize what our retinas actually capture, I'm sure we'd be shocked by how horrible our organic sensors and lenses are, and give due praise to our brains that make consistent simple sense out of crap "hardware". I'm certain that the reason why humans tend to lose their ability to focus at certain distances, seemingly "all at once", because the brain compensates as focus starts to fail, and then at some point can no longer make sense out of the data, so we get a perceptual threshold effect that is probably based on a more subtle and gradual loss of focus.
I find it interesting how much energy our brains waste on obsessing over focus. I've noticed that when I do puzzles like Sudoku, Ken-ken and Kakuro, if I don't have my positive diopter reading glasses, and the paper is slightly OOF, where I can see the lack of perfect focus, but still recognize numbers seemingly as fast as I would with perfect focus, my brain keeps protesting the lack of focus, and I find clues at a much lower rate, and make more mistakes. Same when I play an 8x8 game of minefield on a large monitor, but I am not focused on it. Each clue numeral is easy to see immediately, but the lack of focus just completely breaks down my ability to assimilate information. This would explain why people have such a visceral affinity towards Nearest Neighbor downsampling, and under-sampled captures with large pixels. We did not evolve to see things magnified any larger than proximity alone allows, and our lower-level lizard brain freaks out over perceptual softness in a capture.
Thanks for re-posting the above which, to me, clarifies the matter of appearance of a scene in a viewfinder:
It also covers the case of Sigma's odd-ball "SportsFinder" where what you see is not what all gets captured and also covers a Finder with frame-lines and also covers my Sigma with a viewfinder Magnifier and probably covers Diopter adjustment too.
I am not really concerned about the names, along as it is understood that there are two different concepts here and I was talking about both of them. I have understood the difference for decades, it is other people here who may be conflating the two.
The angle of view of the camera when taking the picture is one thing. It is determined by the size of the sensor and the focal length of the lens.
The angle of view of the viewer when looking at the picture is an entirely different thing. It is determined by the size of the image being viewed and the distance to the viewer's eye.
It is a great pity that these things are not taught in photography books and tutorials in the way that they used to be when I started taking an interest in photography in the 1950s.
1950s? That was way before zooms became feasible and widely available.
Time marches on.
Today, a good smartphone with two-finger zoom is all you need to adjust angle of view to your liking.
You have missed the point. For a viewfinder, the angle of view remains constant, while the angular subject magnification does not (it also depends on the focal length of the camera lens). If I know the angle of view and the coverage, that tells me most of what I need to know about the viewfinder.
Personally, I find the angle of view more intuitive and easier to understand than the viewfinder magnification.
Because the angular subject magnification varies with the focal length, the viewfinder magnification is defined as the angular subject magnification for a 50mm lens. That focal length is quite arbitrary, but has probably been chosen because 50mm is commonly regarded as the "normal" focal length for full frame cameras. However, that means that the definition does not work very well across formats. An MFT camera with a viewfinder magnification of 1.0 will have only about half the angle of view of the viewfinder of a FF camera with a viewfinder magnification of 1.0.