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 ρ of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer find that d is proportional to S 1/n . The value of n is:
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(3)
Sol. d = k ( ρ ) a (S) b (f) c
⇒ [L] = 
0 = a + b
1 = –3a ⇒ a = – 
So b = 
0 = – 3b + c
So n = 3
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