Question

The "luminous flux", or perceived brightness, of a light source is measured in lumens and is inversely proportional to the square of the distance from the light. If a light source produces $200$ lumens at a distance of $3$ meters, at what distance will the light source produce a luminous flux of $25$ lumens?

• A. $6meters$
• B. $30meters$
• C. $6\sqrt{2}meters$
• D. $5\sqrt{2}meters$

Answer 1

Answer: (C)

$6\sqrt{2}meters$

Because the intensity of the light source and the square of the distance are inversely proportional, you can write the product of the "before" intensity and distance squared and the product of the "after" intensity and distance squared. Then set these two products is equal to each other:

$I_1\times d_1^2=I_2\times d_2^2$

${\left(200lumens\right)\left(3meters\right)}^2=\left(25lumens\right)\times d_2^2$

$d_2^2=\frac{\left(20lumens\right){\left(3meters\right)}^2}{\left(25lumens\right)}$

$d_2=6\sqrt{2}meters$