Part of the problem with this subject is the undefined use of the term "perspective". In a purely geometric sense it can be shown that if your position doesn't change, the relative placement of the various objects in your field of view - and your perception of them - doesn't change. It's a simple fact of geometry. Focal length is not a factor.

What focal length does affect is the field of view. As the focal length of a lens increases it has a magnifying effect on what you're seeing (due to the field of view becoming narrower). That magnification affects the perception of distance - including relative distance (and therefore depth) - and the resulting compression effect is often described as a change of perspective - but it's just a narrowing of the area of our attention. That can be proved easily by taking a shot that was captured using a wide angle lens and cropping it to give the same framing as a shot taken with a telephoto lens from the same spot. Apart from a difference in resolution (due to the cropping), they will be exactly the same.

Where our eyes are concerned, you can think of them as behaving like a very wide angle lens with a very small sweet spot. Within the sweet spot the focus, detail perception (resolution), contrast and colour perception are all good, and the further out from the sweet spot you go the worse they all become. At the periphery of our vision our eyes are still capable of detecting movement, large objects and areas of high contrast but almost nothing in the way of fine detail, and provide us with very little colour information.

Where human perception is concerned, another factor that comes into play is our attention. We can change the focus of our attention by changing the direction of our gaze, and in addition to that we can also focus our attention at will within any given field of view (a fixed field of view is what a fixed gaze gives us). The sweet spot is large enough to give us the visual information (the detail, colour, contrast, depth perception etc) that we need when we want to focus our attention on specific areas of interest.

In the case of photographs we want the freedom to choose where within the frame the areas of interest occur, so cameras have to be capable of providing a high level of visual information throughout the frame. Put another way, the sweet spot needs to cover the entire frame (the entire field of view). In reality the very edges of the frame aren't as important as the centre, so where lens design is concerned, the edges of the field of view aren't as critical as the centre, but lenses still get criticised if the edges are soft in any way.

PERSPECTIVE.

So what about the perspective provided by our eyes? To reiterate, focal length affects the field of view but it doesn't affect perspective. What does affect perspective is position. Provided your position doesn't change, the perspective that you get using a short focal length (a wide angle lens) is the same as what you get with longer focal lengths.

One implication of those points is that the human eye doesn't have a unique perspective based on its focal length. The only thing that changes the perspective that we see with our eyes is our position - which changes every time we move. If you want a camera to give you the same perspective that your eyes do, you need only to stand in the same position to take the photograph - focal length is irrelevant.

PERCEPTION.

The sweet spot of our eyes (as described above) corresponds roughly to the area of interest that we get when we focus our attention, which apparently is covered by an angle of view of roughly 40° - 60°. For a full frame (FF) camera, that corresponds roughly to the angle of view provided by a lens with a focal length of ~43mm. So in terms of human perception, a 45mm FF lens will cover the area that corresponds (approximately) to the area of our focused interest, and that in turn corresponds (approximately) to the sweet spot of human eyes (which is only a small part of the wider field of view provided by our eyes).

Put another way, a 45mm FF lens gives us a condensation of what we see with our eyes by isolating the area that we normally focus on and excluding the wider context provided by our peripheral vision.

However, excluding context may not be the photographer's intention, and if his/her intention is to focus the viewer's attention, that can be achieved by other means, the main one being framing. In that context, focal length will often be irrelevant. In addition to that, lenses are usually designed to provide a sweet spot that covers the entire field of view, and that in turn allows areas of interest to be placed anywhere within the frame. In that context, focal length is irrelevant.

Where the perception of distance (and depth) within a photograph is concerned, much depends on how the photograph is viewed. The main relevant factors are the size of the display (the monitor, print or whatever) and the viewing distance. And where the photograph itself is concerned, the degree of cropping is a factor. All of these factors are independent of focal length.

It can be seen from these points that a 45mm (FF equivalent) focal length has very limited significance in photography. However, one of the main things that focal length does do is convey a sense of what the photographer's viewpoint was at the time of capture. The photographer's viewpoint is shared with the viewer, and in that context, the choice of focal length determines the starting point. Bearing in mind that the angle of view can be changed by cropping, we can say that in very general terms a wide angle of view (a short focal length) will give the viewer the impression that they are distanced from the captured scene (or the action), and as the angle of view becomes narrower (as the focal length increases) the viewer is given the impression that they are being brought closer into the scene or closer to the action.

In that context a 45mm FF lens will be good at conveying the sense that the viewer is seeing what they would be seeing if they were standing at a realistic distance from the scene or the action. The relevance of that point will depend very much on circumstance.

Traditionally, magnification of a camera lens has been expressed as (focal length of the actual lens) / (focal length of a "normal" lens). 50mm has usually been used to represent the focal length of a "full frame" 35mm camera, the actual diagonal dimension is closer to 43.5mm, and we have learned in other posts that something like 60mm results in a "natural" perspective, whatever that turns out to mean. Similar calculations are available to estimate the magnification of a telescope, but most astronomers I have known tend to consider magnification as very much a secondary parameter, much less important than light gathering capability (to feed light to various instruments for analysis). So using the ratio of actual distance / apparent distance is probably as good as any. Of note...in some cases. magnification refers to a ratio of linear dimensions. In some cases, it refers to a ratio of apparent areas.

Macro shooters actually calculate magnification correctly by calculating the actual size of the image on the sensor and dividing by the actual size of the original object.

Years ago, I read an non-technical article (probably in Pop Photo) that illustrated the perspective issue brilliantly. I don't remember the details, but it was something like this.

The photographer sat 2 people at opposite ends of a park bench, about 8 feet apart.

He took a picture at slight angle, about 100 feet from the subjects, using a long telephoto lens. In the resulting photo, the subjects appeared to be almost on top of each other, in spite of the fact that they were on opposite ends of the bench.

He then took a second photo with a wide angle lens, moving closer, so that the close subject was about the same size as in the first picture. The two subjects now appeared to be about 15 feet apart, in spite of the fact that they were actually only 8 feet apart.

Now, don't you miss those old photography mags?

Thanks for the explanation. It was speculated earlier in this thread that a FF focal length of 43mm may be the point of crossover for the change from distance compression to distance extension, which, if it were true, would represent the FF focal length that gives a "natural" perception of distance (and depth). And if that was true it would be a suitable reference point for the multiplier-based system used in binoculars and telescopes. It's easy to see that since there's no precise way to determine what a "natural" focal length is, 50mm would have seemed like a fair approximation.