Answer:
Four times
Explanation:
The amount of light collected by a telescope is proportional to the area of the telescope:
[tex]I \propto A[/tex]
However, the area of the telescope is given by
[tex]A=\pi R^2[/tex]
where R is the radius. This means that the amount of light collected is proportional to the square of the radius of the telescope:
[tex]I \propto R^2[/tex]
(a similar argument is valid for the diameter, since radius and diameter are proportional to each other).
In the example, the radius of the 2nd telescope is twice (6 m) as the radius of the first telescope (3 m): this means that the amount of light collected will increase by a factor of
[tex]\frac{I_2}{I_1}=\frac{R_2^2}{R_1^2}=\frac{6^2}{3^2}=\frac{36}{9}=4[/tex]
So, by a factor 4.
