Question

Calculate the magnitude of the faintest object that a 100m optical telescope can detect?

Answer 1

The penetrating power of the telescope is characterized by the limiting magnitude m of the faintest star that can be seen in this instrument.

If the diameter of the telescope

$D=100m=100000mm$

then

$m=2.1+5\cdot \lg{(D)}=2.1+5\cdot \lg{(100000)}=2.1+5 \cdot 5=27.1^m$