Question

A lamp hanging $4$ metres above the table is lowered by $1$ metre. The illumination on the table:

• A. decreased by 25%
• B. increased by 25%
• C. decreased by 66.7%
• D. increased by 77.7%

Answer 1

The correct option is D increased by 77.7%

Illumination intensity at a point $E=\frac{I_o}{d^2}$ where $d$ is the distance of the point from the source

$\therefore$ For $d_1=4$ m, $E_1=\frac{I_o}{4^2}=0.0625I_o$

Now the lamp is lowered by $1$ m, thus $d_2=3$ m

$⟹$ $E_2=\frac{I_o}{3^2}=0.1111I_o$

Percentage increase in illumination intensity $=\frac{E_2-E_1}{E_2}\times 100=\frac{0.1111I_o-0.0625I_o}{0.0625I_o}\times 100$ $=77.7$ %

Thus the illumination is increased by $77.7$ %