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 objectives passes through them,how much larger is the light-gathering power of Yerkes than that of the spyglass?
A) twice
B) 40 times
C) 80 times
D) 400 times

Question

Quizplus · Accepted Answer

The amount of light gathered by a telescope depends on the area of its objective lens. The area of the objective lens of the spyglass is pi(1^2) = pi square inches, while the area of the Yerkes telescope's objective lens is pi(20^2) = 400pi square inches. Therefore, the light-gathering power of Yerkes is (400pi)/(pi) = 400 times larger than that of the spyglass. Hence, the correct answer is D, 400 times.

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