Question

The intensity of light at a distance $r$ from the axis of a long cylindrical source is proportional to :

• A. $r$
• B. $r^2$
• C. $\frac{1}{r}$
• D. $\frac{1}{r^2}$

Answer 1

The correct option is C $\frac{1}{r}$

$\text{Intensity}=\frac{\text{Energy per unit time}}{\text{Area}}$
$=\frac{\text{Power}}{\text{Area}}$
i.e $I=\frac{P}{A}$
Here, area to be taken is the area of the wavefront. In the case of a long cylindrical source, $A\propto r$
$\therefore I\propto \frac{1}{r}$