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 $\mathrm{\rho }$ 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 ${\mathrm{S}}^{\frac{1}{\mathrm{n}}}$ . The value of n is

Hence, the correct answer is 3.