Question

A point source of light moves in a straight line parallel to a plane table. Consider a small portion of the table directly below the line of movement of the source. The illuminance at this portion varies with its distance '$r$' from the source as

• A. $I\propto \frac{1}{r}$
• B. $I\propto \frac{1}{r^2}$
• C. $I\propto \frac{1}{r^3}$
• D. $I\propto \frac{1}{r^4}$

Answer 1

The correct option is C $I\propto \frac{1}{r^3}$

Let the source be S, and the small portion on the table be P.

Let the intensity of source emitted be I.

This intensity is given out spherically symmetrically. So the illuminance at point P becomes,

$E=\frac{I\cos i}{r^2}=\frac{I\left(\frac{d}{r}\right)}{r^2}\propto \frac{1}{r^3}$