Questions

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On a clear day at sea level, the average person can see about 2.9 to 3 miles (4.7 - 5 km) to the horizon.

This limit is caused by the Earth's curvature, not the clarity of the air.

The higher your eye level (such as on a ships deck or cliff) the farther you can see, with 100 foot altitude allowing visibility upto 12 miles away.

A person standing on a beach (eye level 5 ft) sees 2.9 miles, while a person laying down (10 cm off the water) sees only 1.1 km or 0.68 miles.

Obviously you can see tall objects like ships and mountains from much farther away, as they stick up above the horizon.

Fog and haze, or rain can significantly reduce visibility.

Atmospheric Refraction the bending of light can actually make the horizon appear slightly farther away than it geometrically is, usually 3.1 miles (5 km) at sea level.

If you was raised -

10 feet (3 m) you could see 4.4 miles (7 km).

100 feet (30 m) you could see 12.2 miles (20 km).

1,000 feet (305 m) you could see 39 miles (63 km).

To test your mathematics -

How far can you see if you are standing on the beach looking at the horizon?