Many amateur astronomers have telescopes with mirrors 20 cm (1/5 m) in diameter. In comparison, one of the largest astronomical telescopes in the world is the Keck telescope, with a diameter of 10 m. How much greater is the light-gathering power of the Keck telescope than the power of a 20-cm telescope?
A) 50 times greater
B) 7 times greater
C) 125,000 times greater
D) 2500 times greater

Question

Quizplus · Accepted Answer

The light-gathering power of a telescope is proportional to the area of its mirror, which is calculated as πr^2. Comparing the areas (and thus the light-gathering powers) of the two telescopes, the ratio is (5^2) / (0.1^2) = 25^2 = 625. Since the question asks for how much greater, not the total amount, the correct answer is 625 times greater, which is not listed. However, the correct approach to calculate the light-gathering power difference involves comparing the diameters squared (since area ∝ diameter^2 for circles), leading to (10^2) / (0.2^2) = 100 / 0.04 = 2500 times greater.

Many Amateur Astronomers Have Telescopes with Mirrors 20 Cm (1/5