Question

A small lamp having the form of a uniformly luminous sphere of radius R = 6.0 cm is suspended at a height h = 3.0 m above the floor. The luminance of the lamp is equal to L = 2.0.10⁴ cd/m² and is independent of direction. Find the illuminance of the floor directly below the lamp.

Answer 1

See the figure below. The light emitted by an element of the illuminant towards the point O under consideration is

The element dS has the area

The limit of α = 0 to that value for which α + β = 90°, for then light is emitted tangentially. Thus

Substitution gives : E = 25.1 lux