Is the eye equivalent to a 50mm lens?

So in the final post in this series we will look at the adage that a 50mm lens is a “normal” lens because it equates to the eyes view of things. Or is it 43mm… or 35mm? Again a bunch of number seem to exist on the net, and it’s hard to decipher what the real answer is. Maybe there is no real answer, and we should stop comparing eyes to cameras? But for arguments sake let’s look at the situation in a different way by asking what lens focal length most closely replicates the Angle Of View (AOV) of the human visual system (HVS).

One common idea floating around is that the “normal” length of a lens is 43mm because  a “full-frame” film, or sensor is 24×36mm in size, and if you calculate the length of the diagonal you get 43.3mm. Is this meaningful? Unlikely. You can calculate the various AOVs for each of the dimensions using the formula: 2 arctan(d/2f); where is the dimension, and f is the focal length. So for the 24×36mm frame with a 50mm lens, for the diagonal we get: 2 arctan(43.3/(2×50) = 46.8°. This diagonal AOV is the one most commonly cited with lenses, but probably not the right one because few people think about a diagonal AOV. A horizontal one is more common, using d=36mm. Now we get 39.6°.

So now let’s consider the AOV of the HVS. The normal AOV of the HVS assuming binocular vision constraints of roughly 120° (H) by 135° (V), but the reality is that our AOV with respect to targeted vision is probably only 60° horizontally and 10-15° vertically from a point of focus. Of the horizontal vision, likely only 30° is focused. Let’s be conservative and assume 60°.

So a 50mm lens is not close. What about a 35mm lens? This would end up with a horizontal AOV of 54.4°, which is honestly a little closer. A 31mm lens gives us roughly 60°. A 68mm gives us the 30° of focused vision. What about if we wanted a lens AOV equivalent for the binocular 120° horizontal view? We would need a 10.5mm lens, which is starting to get a little fish-eyed.

There is in reality, no single answer. It really depends on how much of the viewable region of the HVS you want to include.