prize8-5, Exercise 2: The horizon for an 80-foot light

Model answer (check the details):

Rule: distance to the horizon in nautical miles is about 1.17 times the square root of the height in feet.

Height 80 feet: the square root of 80 is about 8.94. Multiplying by 1.17 gives about 10.5 nautical miles.

So the light is above the horizon of a sea-level observer at about 10 to 11 nautical miles. A taller observer on a ship's bridge can see it from farther away, because their own horizon adds to the distance (the distances are added together).

Why the real range may differ:
1. Brightness: a weak light may fade from view before the horizon, while a powerful light may be seen as a glow beyond it.
2. Weather: fog, rain or haze reduce the range sharply.
3. Atmosphere: refraction in the air can bend light slightly and extend the range.
4. Background lights: shore lights can hide a navigation light.
5. The observer's height: the higher the observer, the further the range.

Care: the rule is a rough approximation. Official lists of lights give a "nominal range" calculated under defined conditions.