Limiting Magnitude of a Telescope

the numerically largest stellar magnitude that can be distinguished by a given telescope during observations at the zenith. For visual telescopes the limiting magnitude m, can be calculated from the equation

m_v = 5.5 + 2.5 log D + 2.5 log γ

where D is the diameter of the objective in centimeters and γ is the angular magnification of the telescope. The limiting power of photographic telescopes with optimum exposure times can be calculated from the formulas

m_ph = 18.3 + 5 log F for F <5 m

m_ph = 20.1 + 2.5 log F for F >5 m

where Fis the focal length of the telescope in meters.

The limiting magnitude is strongly affected by the background brightness of the sky; by the image quality, which is a function of atmospheric steadiness; by the quality and adjustment of the telescope; and by the properties of the given objective. As a result, the above formulas are only approximate. Modern telescopes are capable of producing astronomical photographs of stars of the 22nd to 24th magnitudes.