Q. A lamp is hanging along the axis of a circular table of radius $r$. At what height should the lamp be placed above the table, so that the illuminance at the edge of the table is $\frac{1}{8}$ of that at its center
A) $\frac{r}{2}$
B) $\frac{r}{\sqrt{2}}$
C) $\frac{r}{3}$
D) $\frac{r}{\sqrt{3}}$
Explanation
(d) $\frac{I_{center}}{I_{edge}} = \frac{\left( r^{2} + h^{2} \right)^{3/2}}{h^{3}}$
$\Rightarrow 8 = \frac{\left( r^{2} + h^{2} \right)^{3/2}}{h^{3}} \Rightarrow 2h = \left( r^{2} + h^{2} \right)^{1/2}$
$\Rightarrow 4h^{2} = r^{2} + h^{2} \Rightarrow 3h^{2} = r^{2} \Rightarrow h = \frac{r}{\sqrt{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.