When positioned at 80 cm and 20 cm from a photometer screen respectively, an electric lamp and a candle generate equal illuminance. The lamp is subsequently covered with a thin paper that transmits 49 % of the luminous flux. By what distance must the lamp be shifted to restore balanced intensities at the screen?

Step-by-step solution

The initial illuminance of the electric lamp and the candle are equal on the photometer screen. I₁ r₁^2 = I₂ r₂^2 I₁ 80^2 = I₂ 20^2 I₁ = 16 I₂ When the lamp is covered with paper, its new luminous intensity becomes I₁' = 0.49 I₁ . To restore balanced intensities, let the new distance of the lamp be r₁' . The illuminance must again be equal: I₁' (r₁')^2 = I₂ r₂^2 0.49 I₁ (r₁')^2 = I₂ 20^2 Substituting I₁ = 16 I₂ : 0.49 16 I₂ (r₁')^2 = I₂ 400 (r₁')^2 = 0.49 16 400 = 3136 r₁' = 56 cm The distance by which the lamp mus