Optics Question 482
Question: A 60 watt bulb is hung over the center of a table 4 m x 4 m at a height of 3 m. The ratio of the intensities of illumination at a point on the centre of the edge and on the corner of the table is
[CPMT 1976, 84]
Options:
A) $ {{(17/13)}^{3/2}} $
B) 2 / 1
C) 17 / 13
D) 5 / 4
Show Answer
Answer:
Correct Answer: A
Solution:
The illuminance at A is $ I _{A}=\frac{L}{{{(\sqrt{13})}^{2}}}\times \cos {\theta _{1}}=\frac{L}{13}\times \frac{3}{\sqrt{13}}=\frac{3L}{{{(13)}^{3/2}}} $.
The illuminance at B is $ I _{B}=\frac{L}{{{(\sqrt{17})}^{2}}}\times \cos {\theta _{2}} $
$ =\frac{L}{17}\times \frac{3}{\sqrt{17}}=\frac{3L}{{{(17)}^{3/2}}} $
$ \therefore $ $ \frac{I _{A}}{I _{B}}={{( \frac{17}{13} )}^{3/2}} $
