Imagine a massive natural phenomena, a continental glacier in this case, hundreds of kilometers wide and 300 meters tall. Approximately how far would this immense wall of ice be visible to the unaided human eye at eye-level height? What if the glacier was 3000 meters tall? How much might the range increase if the glacier-spotter stood on top of a 100-meter hill? Living in a flat, forested landscape, visualizing something like this is tricky for me, and my math skills are woefully lacking. I suppose curvature of the Earth comes into play, eventually.
Good approximate equations here.
Take the first equation there for distance to the horizon,
d=3.57*h[sup]0.5[/sup]
d=distance to horizon, km
h=observer height, m
You would calculate the distance between you and the horizon based on the height of your eyeball. Then you would calculate how far beyond the horizon the glacier is, based on how tall it is.
So if your eyeball is 1.5 meters above ground, then the horizon is 4.37 km away, and the 300-meter-tall glacier is 62 km beyond the horizon. So you’d be able to spot the crest of the glacier from 66.4 km away. (When you’re approaching the Front Range (Denver) from the east on I-76, you can spot the peaks from about 65 miles away; they’re a bit taller than 300 meters, so this is about right.)
3000 meter tall glacier, with you observing from 100 meters up? 231 km away.
Note that that equation is an approximation which will become less accurate for large distances. There is an exact trigonometric equation further down on the Wikipedia page, which I will leave to you to sort out.
Haze in the atmosphere, which may often be there in small amounts even when the air around you appears to be clear, will often obscure distant objects long before the curvature of the Earth becomes an issue. On the other hand, of course, with a clear night sky one can see stars that are millions of light years away.
Apparently the lack of haze on the moon was a bit disconcerting to the Apollo astronauts and demonstrated that human depth perception was not completely based on parallax.