Question

How much more light does an 8-meter telescope gather than a 2-meter telescope? view available hint(s)?

Answer 1

The light gathering of a telescope goes as the area of the telescope, therefore as the square of the aperture:
$P= \frac{D_1^2}{D_2^2}$
where D is the aperture of the telescope.
Therefore, using D1=8 m and D2=2 m, we find
$P= \frac{8^2}{2^2}=16$
So, the larger telescope will collect 16 times more light than the smaller one.