Question

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 centre?

• A. r/2
• B. r/$\sqrt{2}$
• C. r/3
• D. r/$\sqrt{3}$

Answer 1

The correct option is D r/$\sqrt{3}$

$E_2=\frac{1}{8}{E}_1$ or $\frac{1}{(r^2+h^2)}\times \frac{h}{\sqrt{r^2+h^2}}=\frac{1}{8}\frac{1}{h^2}$
(by lambert's cosine law)
or, $(r^2+h^2{)}^{3/2}=(2h{)}^3$ or $(r^2+h^2{)}^{1/2}=2h$
or $r^2+h^2=4h^2$
$h=r/\sqrt{3}$