In a smoke screen of opaque particles with a radius of microns, with a content of g of substance in 1 m of air, visibility is m. How much substance in 1 m of air is sprayed by a curtain source that creates particles with a radius of microns, if visibility is reduced to m?
Solution
Since each thin layer of air with uniform density of polluting particles obstructs the same fraction of light travelling perpendicular to it, the intensity of light decays exponentially over distance, i.e. , where is a characteristic distance depending on the polluting particles. Over a short distance , we have , so is the fraction of area that light is obstructed, i.e.
where is the density of the pollution and and are the mass and the radius of each particle. Thus, in order for different pollutions to cause the same reduction of light intensity over different distances, we must have
If a larger particle has twice the radius of a smaller particle () with the same composition, then its mass is eightfold (). Using m and m, we have g/m g/m.
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