Limiting Magnitude - Calculating Limiting Magnitude

Calculating Limiting Magnitude

Limiting magnitude can be calculated by using a telescope.

As a first approximation, the gain in magnitudes of a telescope is, where D₁ is the diameter of the telescope's primary light gathering component, and D₀ is the diameter of the eye's dark adapted pupil. Both quantities must be measured in the same units. D₀ varies from person to person but is typically 6-7mm (~1/4").

A 10-inch (D₁=254mm) telescope therefore would provide a gain of about 8 magnitudes beyond what could be observed without it. Thus, if one is at a site where the naked eye limiting magnitude (NELM) is 5, the telescope will allow one to see stars as faint as about magnitude 13.

In reality a telescope allows one to see much fainter stars because at higher powers the background is darkened and contrast increased. A typical 10-inch scope at high power (250x or more) will easily reach magnitude 15. See the Telescope Limiting Magnitude Calculator. Derived from this site the formula is

where
D = objective or main mirror diameter in mm
P = power or magnification
t = transmission factor, usually 0.85-0.9.