To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimesional anlysis 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 .

Answer

3

Explanation

`L=(I)^(n)(d)^(y)(f)^(z)`
`L=(M^(1)L^(0)T^(-3))^(x)(M^(1)L^(-3))^(y)(T^(-1))^(2)`
`L=M^(x+y)L^(-3y)T^(-3xx-2)`
`-3y=1 " " x+y=0`
`y=-1/3 " " x-1/3=0`
`x=1/3`
`L=(I)^(1//3)(d)^(-1//3)(f)^(2)`
`n=3`