How much greater is the light-gathering power of the Keck telelscope than that of a 20 cm telescope?

Question

Many amateur astronomers have telescopes with mirrors 20 cm (1/5 m) in diameter. In comparison, the largest astronomical telescope in the world is the Keck telescope, with a diameter of 10 m.

a) 2,500 times larger
b) 125,000 times larger
c) 7 times larger
d) 50 times larger

Answer 1

LGP depends on the area of the objective lens/mirror. Area depends on the square of the diameter. So take the ratio of their diameters (express them both in the same units first!) and square that ratio - that will be your answer.