A photographic plate is positioned directly in front of a small diffused source shaped as a circular disc. Obtaining a good exposure takes 12 s . If the source is rotated by 60^ around one of its diameters, the time required to achieve the same exposure will be

Step-by-step solution

Exposure is given by the product of illuminance and time, H = E t . The illuminance E produced by a small diffused source at a distance r is E = I r^2 , where I is the luminous intensity in the direction of the plate. According to Lambert's cosine law for a diffused source, the luminous intensity at an angle to the normal is I = I₀ . Initially, the plate is directly in front of the source, so = 0^ . E₁ = I₀ 0^ r^2 = I₀ r^2 For a good exposure, H = E₁ t₁ = I₀ r^2 12 . When the source is rotated by 60^ , the angle be