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To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes

To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density p of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that d is proportional to Sn. The value of n is

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