## Calculus 8th Edition

By moving halfway to the lamp, $x$ is divided by $2$. Thus, by the inverse square law: $f(x) = k(\frac{x}{2})^{-2}$ $f(x) = \frac{k}{\frac{x^2}{2^2}}$ $f(x) = \frac{k}{\frac{x^2}{4}}$ $f(x) = \frac{4k}{x^2}$ Which means there is 4 times as much illumination, or the light is four times as bright.