The distance to the visible horizon depends upon the height of eye. From the bridge of most ships that I sailed on it was considered to be roughly six miles.
And what happened when you looked through a pair of binoculars? How about some really strong binoculars?
Well, I don’t know if you consider this to be an average binocular:
We called them ‘Big Eyes’ and i could read newsprint from a mile away on the USS Holland’s set.

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A similar pair...Nikon 20x120 IV Telescopic Binoculars
Powerful 20x magnification is ideal for extreme long-range terrestrial use or for lunar and planetary viewing or wide-field comet hunting 