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Comment by mannykannot | Hacker News Reader

I wonder whether that is entirely so (though the difference may not be relevant for the intended applications of this lens.) The reason I say this is that one can often tell whether a telephoto lens is being used at long range, as opposed to a normal lens at shorter distance, by the way the former seems to compress the longitudinal axis (at least when one is watching a movie rather than a still image.) This effect seems to me to be independent of focal depth, in that it does not seem to depend on having nearby or distant objects markedly out-of-focus, though I may be mistaken about this. Do magnified long-distance movies shot with normal focal-length lenses look like their telephoto equivalents?

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Yes, mathematically telephoto is exactly just cropped wide angle. The same light field is falling on the front element of either lens so, modulo focus effects and distortion, it could not be otherwise.

(Differing projections/distortions such as fisheye are likewise exactly equivalent to mathematical transforms for the same reason.)

You can see that this is true when using a (physical) zoom lens. When zooming, there is no change in the projected image of any sort other than it simply grows larger.

The effect you are referring to is complementary to parallax and is likewise due exactly to physical proximity to or distance from the subject being photographed. (Telephoto lenses require the subject to be further away to remain in the frame; in doing so, they move relatively closer to the background, thus longitudinally compressing the scene.)

The source of that compression effect is the relative distances top the sensor of different elements in the picture - so a result of long vs short range, rather than long vs short focal length. At a long range, your nose is 1% closer to sensor than your eyes are. At a _really_ close range, it's maybe 50% closer to the sensor than your eyes are. Given a fixed range, though, you can achieve the same look by using a long lens, or by cropping a shot taken with a shorter lens.

The thing is, distance and focal length aren't independent. People don't usually shoot long lenses in close quarters, and don't shoot distant subjects with wide angle lenses, we just tend to fill our frames with the subject. That means the compression effect is technically not related to focal length, but in practice ends up showing up more when using longer lenses.

> Do magnified long-distance movies shot with normal focal-length lenses look like their telephoto equivalents?

Generally, I think the answer is yes. But the more complicated answer is that every lens design has its own flavor of distortion. An image from a lens optimized for telephoto shots is going to have slightly different characteristics than a cropped image from a lens optimized for wide shots.

The compressed effect I think you are referring to is likely attributable to perspective, most noticeable when the movie does one of those zoom shots where they keep the subject at the same relative size in the frame while moving the camera in or out. Like on this shot: https://youtu.be/in_mAvHu9E4?t=19

This is definitely a real effect. I can’t doodle this out right now but if you grab a piece of paper and draw out the triangles for a pinhole camera with different focal lengths you can see how the angles (and horizontal separation at the image plane) are quite different with different focal lengths.

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