Question

A lamp is hanging at a height of $40cm$ from the centre of a table. If the height of the lamp is increased by $10cm$, then the illuminance on the table.

• A. Increases by $10$%
• B. Decreases by $10$%
• C. Increases by $36$%
• D. Decreases by $36$%

Answer 1

The correct option is D Decreases by $36$%

Illuminance, $I=\frac{L}{r^2}$
$\therefore I_1=\frac{L}{1600}$ and $I_2=\frac{L}{2500}$
$\therefore$ % Decrease in illuminance
$=\left(\frac{I_2-I_1}{I_2}\right)\times 100$
$=(1-\frac{1600}{2500})\times 100$
$=\frac{900}{2500}\times 100=36$.