Optics Question 487
Question: A small lamp is hung at a height of 8 feet above the centre of a round table of diameter 16 feet. The ratio of intensities of illumination at the centre and at points on the circumference of the table will be
[CPMT 1984, 1996]
Options:
A) 1 : 1
B) 2 : 1
C) $ 2\sqrt{2}:1 $
D) 3 : 2
Show Answer
Answer:
Correct Answer: C
Solution:
Illuminance at A, $ I _{A}=\frac{L}{h^{2}} $
Illuminance at B, $ I _{B}=\frac{L}{\sqrt{{{(h^{2}+r^{2})}^{2}}}}\cos \theta $
$ =\frac{Lh}{{{(r^{2}+h^{2})}^{3/2}}} $
$ \therefore \frac{I _{A}}{I _{B}}={{( 1+\frac{r^{2}}{h^{2}} )}^{3/2}} $
$ ={{( 1+\frac{8^{2}}{8^{2}} )}^{3/2}}={{2}^{3/2}}=2\sqrt{2}:1 $
