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 $$\rho $$ 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 S^1/n. The value of n is

During Searle's experiment, zero of the Vernier scale lies between 3.20 $$ \times $$ 10^-2 m and 3.25 $$ \times $$ 10^-2 m of the main scale. The 20^th division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 $$ \times $$ 10^-2 m and 3.25 $$ \times $$ 10^-2 m of the main scale but now the 45^th division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 $$ \times $$ 10^-7 m². The least count of the Vernier scale is 1.0 $$ \times $$ 10^-5 m. The maximum percentage error in the Young's modulus of the wire is