The intensity of light $I$ at a distance $d$ from a source follows an inverse proportionality. If $I=400,{\text{W/m}}^2$ at $d=2,\text{m}$, what is $I$ at $d=5,\text{m}$?

Step-by-step solution

1. Use the relation $I_1{d}_1=I_2{d}_2$ because $Ipropto\frac{1}{d}$.
2. Substitute known values: $400\times 2=I_2\times 5$.
3. Solve for $I_2$: $I_2=\frac{400\times 2}{5}=160$ W/m${}^2$.
4. Round to appropriate significant figures (none needed here).

Concept tested: Inverse Proportion

Published 7 October 2026 · How this solution was prepared and checked