Question

Calculate the magnitude of the faintest object that can be detected by an optical
telescope of diameter 5.0 m.

Answer 1

Solution. The Scope's Star Magnitude Limit we can find using formula

$$L_{mag}=2^m+5log(D_0)$$

where Lmag is the magnitude limit of the scope; D0 is objective or main mirror diameter in mm. Therefore

$$L_{mag}=2^m+5log(5000)=20.5^m$$

Answer.

$$L_{mag}=20.5^m$$