A small refracting "spyglass" telescope has an objective lens with a diameter of 2 inches. The world's largest refracting telescope at Yerkes Observatory has an objective lens with a diameter of 40 inches. Assuming that all light striking the objective lenses passes through them, how much larger is the light-gathering power of Yerkes than the spyglass?
A) twice
B) 40 times
C) 80 times
D) 400 times

Question

Quizplus · Accepted Answer

The light-gathering power of a telescope is proportional to the area of its objective lens. The area of a circle (which is the shape of the lens) is given by πr^2, where r is the radius. Since the diameter is twice the radius, a lens with a diameter of 40 inches has a radius 20 times larger than a lens with a diameter of 2 inches. Because the area goes with the square of the radius, the Yerkes telescope gathers (20^2) = 400 times more light than the spyglass.

A Small Refracting "Spyglass" Telescope Has an Objective Lens with a Diameter