An observer is standing on a plane at h metres below the centre of a reflecting sphere of radius r. Another object on the plane is perceived at an angle α from the vertical. What is α of the horizon in terms of h and r?

Solution

The angle α=arccos((r+√(r²+8h²))/4h).

Poem

The flat earth
It could be in fact that the earth is flat
There are some theories
And you can read some poetry
Looking down up to the sky
The earth was flat after all
Said I
Am I right or am I wrong ?
Turning to the horizon
Suddenly I found
The planet is still on the ground

Bella