Question

A 20. cm telescope collects how many times the light collected by a 5.0 cm telescope?

Answer 1

The light collected by a telescope is proportional to the area of the telescope.

The area of a telescope is π * (Diameter / 2) ^2 = π * (Diameter)^2 / 4.

So, for the 20.0 cm telescope, area = π * (20.0cm)^2 / 4.

And for the 5.0 cm telescope, area = π * (5.0 cm)^2 / 4

So, divide both expressions to find the ratio of collection of light of one telescope to the other:=> (20.0)^2 / (5.0)^2 = (20.0 / 5.0)^2 = 4^2 = 16

Then, the 20.0 cm telescope collects 16 times the ligth that the 5.0 cm telescope collect.    <--- answer