As you can see, the frame includes only a fraction of what the eye sees. The normal (50mm equivalent) lens covers an angle of about 46 degrees, measured diagonally across the frame. The angle of view of the human eye is on the order of 210 degrees, and that is without moving the fixation point.
You might say: the claim about normal lenses was meant to be restricted to our sharp central vision. But that cannot be right either: the angle of foveal, sharp vision is only 1.5–2 degrees. The angle of macular vision (where things are still somewhat sharp) is only about 17 degrees. What makes a lens normal must therefore be something different. It has to do, I submit, with conventions about viewing conditions.
Most people these days, photographers included, don’t fuss over viewing conditions. Photos taken with vastly different lenses all get enlarged to various sizes and viewed from various distances—in an album, a book, a gallery, or on a smartphone—without any consideration for the focal lengths involved. But there is one particular viewing condition that was considered normal long ago when prints were the preferred currency of photography. And for that condition, the normal lens stands out as the right focal length to produce photos that look spatially natural—or perspectivally correct—when viewed under that condition.
Here is how it works. Once upon a time, the standard print size for photographs was 8" x 10". When you hold an 8" x 10" print at a comfortable reading distance, which for most people is in the 14"–16" range, the distance between eye and print is slightly greater than the print diagonal, which is 13". Likewise, the focal length of a normal lens is slightly greater than the film diagonal. Therefore the geometric relationship between eye and print is the same as the relationship between normal lens and film (or sensor). In fact, the correspondence is extremely close. If we let the reading distance fall in the middle of the range, at 15”, then it exceeds the print diagonal by a factor of 15/13. Multiply the diagonal of a 35mm frame by 15/13 and you get 49.6mm! So stop complaining about 50mm being too long for a normal lens. (Homework assignment: a 35mm negative’s aspect ratio of 2/3 does not exactly match the 4/5 print ratio. How does that affect the argument?)
To recap: if you hold an 8" x 10" print from a 35mm negative exposed with a 50mm lens at reading distance, then everything will look spatially natural. The print is a perspectivally sound representation because it works exactly like Alberti’s window.
It so happens that a normal lens is also the easiest and cheapest focal length to design and manufacture, which helps explain how it became everybody's first lens. I don’t know whether there is a deeper cause for this coincidence or whether Alberti’s ghost simply ordained it.
Wide-angle lenses
As I said, we tend to view photos taken with wide-angle and telephoto lenses in the same manner as we view photos taken with a normal lens. Consequently, we view wide-angle photos from farther away than their viewpoint, and we view long-lens photos from too close up. This is where the lore of perspectival distortion originates. Mantegna’s Christ looks distorted, all right, but as we saw, this is no flaw of the painting but a consequence of our looking at it from too close.
If you want to use a telephoto lens and show convincing depth, you must place your viewers in the right position. This means, you must either show very small prints or else keep people at a distance. But this is not what you bought that big expensive lens for. So the lens is a poor choice for conveying space. A normal lens is good with respect to perspective under normal viewing conditions. But it is often still too narrow to capture what we are interested in. So we are forced into using wide-angles. What about their distortions?
Let’s begin by convincing ourselves that, as with telephoto-lenses, the distortion is not a lens defect but the consequence of looking at the photo from the wrong distance.