Question

The illumination (i) of a lamp on a screen is inversely proportional to the square of distance (d) of the screen form the lamp, When d = 5 i = 1, find the value of i when d = 2.5.

Answer 1

$i\alpha \frac{1}{d^2}$
$i=\frac{k}{d^2}$
$$\begin{gathered} \mathrm{When}\mathrm{d}=5\mathrm{and}\mathrm{i}=1, \\ 1=\frac{\mathrm{k}}{25} \\ \Rightarrow \mathrm{k}=25...\left(\mathrm{i}\right) \\ \mathrm{When}\mathrm{d}=2.5, \\ \mathrm{i}=\frac{25}{(2.5{)}^2}[\mathrm{From}(\mathrm{i}\left)\right] \\ \Rightarrow \mathrm{i}=\frac{25}{(2.5{)}^2}=4 \end{gathered}$$