Two light sources having intensities of 8 cd and 12 cd are positioned on the same side of a photometer screen, at a distance of 40 cm from it. At what distance must an 80 cd source be placed to balance the illuminance?

Step-by-step solution

The illuminance E produced by a point source of luminous intensity I at a distance r is given by E = I r^2 . Since the two sources of 8 cd and 12 cd are placed on the same side of the photometer screen at the same distance, their combined illuminance is the sum of their individual illuminances: E₁ = I₁ r₁^2 + I₂ r₁^2 = 8 40^2 + 12 40^2 = 20 40^2 Let the 80 cd source be placed at a distance r₂ on the opposite side to balance the illuminance. The illuminance produced by this source is: E₂ = I₃ r₂^2 = 80 r₂^2 For the