Optics Question 480
Question: A bulb of 100 watt is hanging at a height of one meter above the centre of a circular table of diameter 4 m. If the intensity at a point on its rim is $ I _{0} $ , then the intensity at the centre of the table will be
[CPMT 1996]
Options:
A) $ I _{0} $
B) $ 2\sqrt{5}I _{0} $
C) $ 2I _{0} $
D) $ 5\sqrt{5}I _{0} $
Show Answer
Answer:
Correct Answer: D
Solution:
The illuminance at B $ I _{B}=\frac{L}{1^{2}} $ …….(i) and illuminance at point C $ I _{C}=\frac{L\cos \theta }{(\sqrt{5{{)}^{2}}}}=\frac{L}{(\sqrt{5{{)}^{2}}}}\times \frac{1}{\sqrt{5}} $
$ \Rightarrow \ \ I _{C}=\frac{L}{5\sqrt{5}} $ …… (ii) From equation (i) and (ii) $ I _{B}=5\sqrt{5}\ I _{0} $
