Optics Question 501
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 center
[MP PET 2005]
Options:
A) $ \frac{r}{2} $
B) $ \frac{r}{\sqrt{2}} $
C) $ \frac{r}{3} $
D) $ \frac{r}{\sqrt{3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{I _{center}}{I _{edge}}=\frac{{{(r^{2}+h^{2})}^{3/2}}}{h^{3}} $
$ \Rightarrow 8=\frac{{{(r^{2}+h^{2})}^{3/2}}}{h^{3}} $
$ \Rightarrow 2h={{(r^{2}+h^{2})}^{1/2}} $
$ \Rightarrow 4h^{2}=r^{2}+h^{2} $
$ \Rightarrow 3h^{2}=r^{2} $
Therefore $ h=\frac{r}{\sqrt{3}} $
