Question

The distance of an illuminated object from its light source is decreased to 1/3 while the luminous flux remains constant. Which is true of the illuminance on the object?1) The illuminance will be tripled.2) The illuminance will be multiplied by 9.3) The illuminance will be divided by three.4) The illuminance will be doubled.

Answer 1

Illuminance is inversely proportional to the square of the distance from the light source.

Then, if we decrease the distance to 1/3, the illuminance will grow up to a factor of 1/(1/3)^2:

$\frac{1}{(\frac{1}{3})^2}=\frac{1}{(\frac{1}{9})}=9$

Therefore, the answer is:

2) The illuminance will be multiplied by 9.