You wish to read by the light of a lamp with a single lightbulb at your desk. In order to get the same brightness on the page from a 25 W bulb as you can from 100 W bulb, how much closer do you need to bring the lamp to your book? Assume that the light bulbs are equally efficient.
A) 1/2 the distance
B) 1/8 the distance
C) 1/4 the distance
D) 1/16 the distance

Question

Quizplus · Accepted Answer

The brightness or illumination of a surface by a light source follows the inverse square law, which states that the illumination (I) is inversely proportional to the square of the distance (d) from the source, $I \propto \frac{1}{d^2}$. To achieve the same brightness with a quarter of the power (25 W compared to 100 W), you need to decrease the distance by a factor that, when squared, equals 4 (since $100 W / 25 W = 4$). Therefore, you need to bring the lamp to 1/2 the original distance, because $(1/2)^2 = 1/4$, which compensates for the reduced power of the bulb.

You Wish to Read by the Light of a Lamp