How to calculate the viewing distance giving natural perspective?

When I move my eye closer to a photograph, it will fill a larger part of my view. When I move further, the area filled by the image will become smaller. Apparently, there must be some point where the angle of view filled by the image is the same as was the angle of view for the lens when the image was originally taken.

I have seen the claims such as "a 50mm (35mm equivalent) lens will give the same perspective as human eye", but this seems to imply some certain combination of output media and viewing distance that I've never seen accompanied with the claims. An older question addresses the optimal viewing distance by resolution and sharpness, but those are not my current concern.

How can I calculate the distance x, where my eye should be from an image with diagonal d, shot with a lens with 35mm equivalent focal length f, to have it fill the same angle of view as it was originally filling from camera's point of view?

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The question Why does a 50mm lens appear to give a human field of view? touches on those claims you mention. – mattdm Nov 30 '12 at 14:08
And, I think How to capture the scene exactly as my eyes can see? is trying to ask the same thing as your question, but is asked from a less technical background and therefore in a kind of vague way (and therefore that question has lots of answers covering related "as the eye sees" issues like dynamic range and depth of field). – mattdm Nov 30 '12 at 14:09

The formula you're asking for is

``````x = (fl * d) / s
``````

Where `s` is the diagonal size of the image sensor — 43.3mm for a full frame sensor.

However, for a 12" x 8" landscape print from a 24mm lens, your viewing distance works out to be about 8 inches — not exactly comfortable — and that's if  your eyes can actually focus properly.

A picture being flat means its perspective remains the same whatever your viewing distance, so I wouldn't worry about trying to match up the field of view. The whole thing about 50mm lenses giving the same perspective as the human eye just means the view through the viewfinder is not enlarged, or shrunk, and that if you open your left eye the view you get is pretty much the same. The eye actually has a much wider field of view than a 50mm lens.

There is something to be said of moving images which fill your eye's entire angle of view, giving you an enhanced sensation of movement. This is the principle IMAX cinemas are based on. For still images you don't get the same effect.

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Where it does make a significant difference is with very wide angle rectilinear images. Take a large group/team shot taken with, say, a 20-ish mm lens on a full-frame camera (due to space constraints)—the people at the frame edges will be considerably distorted unless you put your eye in a position geometrically equivalent to where the camera was in the original scene. (A picture taken in a constrained space is best viewed large in an equally-constrained space, like a corridor, since viewers will not notice the foreshortening nearly as much.) – user2719 Nov 30 '12 at 12:46

I have seen the claims such as "a 50mm (35mm equivalent) lens will give the same perspective as human eye", but this seems to imply some certain combination of output media and viewing distance that I've never seen accompanied with the claims.

No, those claims do not presume any particular output media and/or viewing distance. The claim that is made is that, with a 50mm lens, the frame of a 35mm film (or the sensor of a FF camera) will capture the same image as a human eye located at the same position and focussed on the same object.

This is completely unrelated to how the image is later viewed, but has more to do with how we humans perceive objects in 3-dimensional space, using only 2-dimensional measurement equipment (our eyes).

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