How much more light does a 1 m telescope gather than a 10 cm telescope How many magnitudes fainter should be detectable by a 1 m telescope than by a 10 cm telescope?

Answer 1

The light-gathering power of an objective lens or mirror is proportional to its area, or equivalently,
to the square of its linear dimensions (radius, diameter, circumference).

If the focal ratios ('f' number) are the same, then the 1-m scope scoops up 102 = 100 times as much light
as the 10-cm job.

100 times difference in brightness is exactly the mathematical definition of six (6) magnitudes brighter/dimmer.

Answer 2

A 1 m telescope gathers 100 times more light than a 10 cm telescope since the area of the aperture is proportional to the square of the diameter. This means that a 1 m telescope can detect objects that are 5 magnitudes fainter than a 10 cm telescope since each magnitude corresponds to a factor of 2.5 in brightness.