Answer
The illumination is $i=2.4\text{ foot-candles}$ at a distance of 50 feet.
As per the question $i\propto \frac{1}{{{d}^{2}}}$.
Work Step by Step
That means $i=\frac{k}{{{d}^{2}}}$
Where i is illumination, d is the distance and k is the constant.
Now, calculate the value of k,
$\begin{align}
& i=\frac{k}{{{d}^{2}}} \\
& 3.75=\frac{k}{{{(40)}^{2}}} \\
& k=3.75{{(40)}^{2}} \\
& k=6000 \\
\end{align}$
Substituting the value of k and d in $i=\frac{k}{{{d}^{2}}}$.
$\begin{align}
& i=\frac{6000}{{{d}^{2}}} \\
& i=\frac{6000}{{{(50)}^{2}}} \\
& \ i=\frac{6000}{2500} \\
& i=2.4\ foot-candles
\end{align}$
Therefore, the illumination is $i=2.4\text{ foot-candles}$ at a distance of 50 feet.
