Question

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

Answer 1

Solution:

As a first approximation, the gain in magnitudes of a telescope is

Limiting magnitude = 5 log₁₀ (D₁ / D₀) = 5 log10 (5 m / 0.006 m) = 14. 6 m

here D₁ is the diameter of the telescope's primary light gathering component, and D₀ is the diameter of the eye's dark adapted pupil.

Answer: 14.6 m