Question

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?

Answer 1

40 times

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 :

`A=\pi r^2`

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

`A=(\pi d^2)/(4)`

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,

`(K)/(A)=(10\ m)/(0.25\ m)\\\\(K)/(A)=40\\\\K=40* A`

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