When positioned 5 cm away from a weak point source, a photographic plate requires an exposure time of 3 s . If the plate is instead located at a distance of 10 cm from the source, the duration required to achieve an identical exposure would be

Step-by-step solution

Exposure is given by the product of intensity and time, E = I t . For a point source, intensity is inversely proportional to the square of the distance, I 1 r^2 . For identical exposure, I₁ t₁ = I₂ t₂ . t₁ r₁^2 = t₂ r₂^2 t₂ = t₁ ( r₂ r₁ )^2 Substituting the given values r₁ = 5 cm , r₂ = 10 cm , and t₁ = 3 s : t₂ = 3 ( 10 5 )^2 t₂ = 3 2^2 = 12 s