As a result of my post on the flat-Earth believers, I was struck by their claim that when you look into the distance, you do not see the Earth’s curvature. This raised in my mind the question of, if you look out over a flat expanse, say a desert or an ocean or from a plane, how far can you see? It may seem as if we can see really far, especially since we can see distant stars, but many factors introduce a great deal of variability.
In order to ‘see’ something at a distance, what we are seeing is light from the sun that has been reflected from that object and has come in a straight line right into our eyes. So the first factor at play is the contrast between the object and its surroundings. We judge that a mountain range is distant because it looks muted compared to objects that are nearer. This is why it is so hard to gauge distances in whiteout conditions in a snowstorm or dust storm. For example, see this video of a dog being tossed out of an airplane. (Don’t worry, nothing bad happens! The reason that the snow looks like distant clouds is the lack of contrast that makes judging of distance hard.)
Another major factor is the scattering of light. The atmosphere contains oxygen, nitrogen, and water vapor molecules plus dust and other particulates. Some of the light coming to us from the distant object gets scattered by these things into other directions and no longer reaches our eyes, thus reducing the visibility of the object. But in addition, sunlight also falls on all these intervening particles between the object and us and also gets scattered, and some of that scattered light will come in the same direction and enter our eye. So this scattering (called Rayleigh scattering) affects visibility in two ways: it reduces the amount of light coming to us from the distant object, and it introduces extraneous light into that same path. All these factors reduce the visibility of the distant object and sets a limit on how far we can see.
Meteorologists have something called the extinction coefficient that enables you to calculate how far you can see. If the atmosphere is completely free of particulates, leaving only the molecules of air, then you can see a distance of about 300 km. In actual practice, if you can see up to 50 km, the atmosphere is said to be “exceptionally clear”.
(Ref: “On a Clear Day You Can’t See Forever” in the book Clouds in a Glass of Beer (1987) by atmospheric physicist Craig F. Bohren.)