question_answer

A 60 watt bulb is hung over the center of a table 4 m ´ 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]

A)            \[{{(17/13)}^{3/2}}\]         

B)            2 / 1

C)            17 / 13                                     

D)             5 / 4

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 \[{{I}_{B}}=\frac{L}{{{(\sqrt{17})}^{2}}}\times \cos {{\theta }_{2}}\] \[=\frac{L}{17}\times \frac{3}{\sqrt{17}}=\frac{3L}{{{(17)}^{3/2}}}\]  \[\therefore \] \[\frac{{{I}_{A}}}{{{I}_{B}}}={{\left( \frac{17}{13} \right)}^{3/2}}\]