How much more light can the Keck telescope (with its 10-m diameter mirror) gather than an amateur telescope whose mirror is 25 cm (0.25 m) across?

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 :

r is radius, r = d/2 (d=diameter of the mirror)

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,

It means that Keck telescope will gather 40 times light than amateur telescope.

b

step-by-step explanation: