A point source of light travels in a straight line parallel to a...

Let $h$ be the constant height of the point source above the plane table.

The illuminance $E$ at a small portion of the table is given by $E = \dfrac{I_0 \cos \theta}{r^2}$, where $I_0$ is the luminous intensity of the source, $r$ is the distance between the source and the portion, and $\theta$ is the angle of incidence.

Since the small portion is directly beneath the line of motion of the source, the vertical distance from the source to the table is $h$.

From the geometry of the setup, the angle of incidence $\theta$ satisfies $\cos \theta = \dfrac{h}{r}$.

Substituting this into the formula for illuminance, we get:

$E = \dfrac{I_0}{r^2} \left(\dfrac{h}{r}\right) = \dfrac{I_0 h}{r^3}$

Since $I_0$ and $h$ are constants, the illuminance varies with the distance $r$ as $E \propto \dfrac{1}{r^3}$.