Like the measurements of Aristarchus and Eratosthenes, this calculation of Alhazen is simple enough in theory.

Its defect consists largely in the difficulty of fixing its terms with precision, combined with the further fact that the rays of the sun, in taking the slanting course through the earth's atmosphere, are really deflected from a straight line in virtue of the constantly increasing density of the air near the earth's surface.

Alhazen must have been aware of this latter fact, since it was known to the later Alexandrian astronomers, but he takes no account of it in the present measurement.

The diagram will make the method of Alhazen clear.
His important premises are two: first, the well-recognized fact that, when light is reflected from any surface, the angle of incidence is equal to the angle of reflection; and, second, the much more doubtful observation that twilight continues until such time as the sun, according to a simple calculation, is nineteen degrees below the horizon.

Referring to the diagram, let the inner circle represent the earth's surface, the outer circle the limits of the atmosphere, C being the earth's centre, and RR radii of the earth.