Problem 5.12

A small lamp having the form of a uniformly luminous sphere of radius \(R=6.0 \mathrm{~cm}\) is suspended at a height \(h=3.0 \mathrm{~m}\) above the floor. The luminance of the lamp is equal to \(L=2.0 \cdot 10^{4} \mathrm{~cd} / \mathrm{m}^{2}\) and is independent of direction. Find the illuminance of the floor directly below the lamp.