A 450 cd light source creates an illumination of 30 lux at a distance of three meters.

A 450 cd light source creates an illumination of 30 lux at a distance of three meters. Determine the angle of incidence of the luminous flux.

To find out the angle of incidence of the luminous flux under consideration, we use the formula: E = I * cosφ / r ^ 2, from where we express: cosφ = r2 * E / I and φ = arccos (r2 * E / I).
Data: r – distance to the used light source (r = 3 m); E – created illumination (E = 30 lux); I – luminous intensity (I = 450 cd).
Let’s perform the calculation: φ = arccos (r ^ 2 * E / I) = arccos (3 ^ 2 * 30/450) = arccos 0.6 ≈ 53.13º.
Answer: The angle of incidence of the considered luminous flux is 53.13º.