It’s not really about “zoom.” It’s about detail, or to put it in digital terms, “resolution.”
I’m making these figures up, but basically if your natural vision is 1080p, an eagle has 16K super-duper-holy-shit HD vision. To you, that rabbit 200 yards away is *at most* a single pixel (probably even less), which isn’t enough information to register it to you as “rabbit.” But that eagle can see the ears, the tail, the legs, even the eyes of that rabbit, so it *definitely* knows what it’s looking at.
So, a memorable lecture in first year physics tackled this, and it turns out that yes, eagles do have more light receptor cells packed into their retinas, however they only have marginally better detailed vision than humans do.
Why? When light passes by a sharp threshold like a slit, or an iris, abberation happens. The smaller the aperture, the more abberation, and the less detailed the image can possibly be. Eagle eyes are only so big, so this abberation limits the maximum distance it is possible to see clearly.
Eagles are NOT seeing in 4K resolution, spotting crystal clear mice from miles away. This is physically impossible. What they ARE doing is being VERY sensitive to changes in the fovea, so a distant mouse crossing a field is a very obvious black dot moving around whereas we humans would not have the sensitivity to pick this motion up.
Another element of this is the literal neural network their eyes are attached to. The ability to “see” a rabbit in a field a mile away is as much the impressive data captured by their eyes as it is the neurons interpreting that data into “there’s a rabbit in that field”. Consider that a human could be staring at a rabbit several feet away and fail to “see” it.
Many raptors (large birds of prey) like eagles have a special adaptation called a “convexiclivate” fovea. Like ourselves, they have a location where receptors are at their highest density,and where overlying material is also moved aside, making a pit or depression, what “fovea” means. Then, the raptors go a step further, filling the pit with a medium (the clear jelly stuff inside the eye, “the vitreous”, which means glasslike) that has a greater refractive index just in the pit than the rest of the eye. This takes the light coming in through the top of the pit and spreads it out, a built in mini-telescope. Better geometry for distant vision!
Perhaps the eagle just spotted something that could have been a rabbit, and just flies down for a closer look. As he gets closer he sees it’s an animal like a wolf. And he veers off. No one interviews the eagle who’s been fooled. A hungry eagle is gonna check out everything that might be lunch; I’ll give him that. But resolving power in any optical system limits what can be identified for sure.
Eagles have 20/5 vision
Humans have 20/20 vision.
So to see something 20 feet away, we need to be 20 feet away.
Eagles can see something from 20 feet away, that we need to be 5 feet away from to see.
This means that while you need to sit 50 cm away from your screen to see it clearly, an eagle can sit a bit over 2 meters away, and still read everything on the screen clearly.
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