Limiting Magnitudes of Telescopes

Limiting Magnitudes of Telescopes of Different Apertures
D [in]	D [cm]	m_vL
*No Telescope, D_{eye's pupil}* = 0.7 cm**		6.2 (assumed average value, with exceptional eyesight, a very dark, moonless sky and total dark adaptation this might be 6.5)
1	2.5	9.0
2	5.1	10.5
6	15	12.9
12	30	14.4
24	61	15.9
60	150	17.9
100	254	19.0
150	380	19.9
200	508	20.5
236	600	20.9
These estimates, based on the relationships m_vL(D) - m_vLeye = 2.5 log(D/D_eye)² Þ m_vL(D) = 6.97 + 5 log D [cm] = 9.00 + 5 log D [in], indicate the limiting magnitudes that might be visible to an observer looking through a telescope's eyepiece under ideal conditions. These magnitudes are very optimistic because light losses within the telescope have been ignored and ideal observing conditions are seldom realized. In most cases, more realistic limiting magnitudes would be 1 to 2 magnitudes brighter. Photographic emulsions and especially CCDs could capture substantially fainter images than these.