Answer :
Answer:
40 times
Step-by-step explanation:
It is given that,
The aperture of Keck telescope, d₁ = 10 m
The aperture of the amateur is 25 cm or, d₂ = 0.25 m
Gathered light is directly proportional to the area of the mirrors as :
[tex]A=\pi r^2[/tex]
r is radius, r = d/2 (d=diameter of the mirror)
[tex]A=\dfrac{\pi d^2}{4}[/tex]
It is directly proportional to the diameter of the mirrors.
On taking ratios of the area of both mirrors, we can get the ratio of light gathered.
So,
[tex]\dfrac{K}{A}=\dfrac{10\ m}{0.25\ m}\\\\\dfrac{K}{A}=40\\\\K=40\times A[/tex]
It means that Keck telescope will gather 40 times light than amateur telescope.