Q. A $60\ watt$ bulb is hung over the center of a table $4\ m \times 4\ m$ at 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
A) $(17/13)^{3/2}$
B) $2/1$
C) $17/13$
D) $5/4$
Explanation
(a) The illuminance at $A$ is
$I_{A} = \frac{1}{\left( \sqrt{13} \right)^{2}} \times \cos\theta_{1} = \frac{L}{13} \times \frac{3}{\sqrt{13}} = \frac{3L}{(13)^{3/2}}$
The illuminance at $B$ is
$I_{B} = \frac{L}{\left( \sqrt{17} \right)^{2}} \times \cos\theta_{2}$
$= \frac{L}{17} \times \frac{3}{\sqrt{17}} = \frac{3L}{(17)^{3/2}}$
$\therefore\frac{I_{A}}{I_{B}} = \left( \frac{17}{13} \right)^{3/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.