Telescope Magnification, Exit Pupil, Dawes' Limit & Bortle Calculator (2026)

Because light waves diffract when passing through a finite circular aperture, every point star forms an Airy disk surrounded by diffraction rings. Once magnification exceeds roughly 2× per millimeter of aperture (50× per inch)—corresponding to a 0.5mm Exit Pupil—you are merely magnifying the blurry Airy diffraction disk without resolving any new fine detail ('empty magnification').

Exit Pupil is the diameter of the cone of light exiting the eyepiece: Exit Pupil (mm) = Aperture (mm) ÷ Magnification (or Eyepiece Focal Length ÷ Telescope Focal Ratio). A dark-adapted young human eye dilates to ~7mm; if the exit pupil exceeds 7mm, light hits the iris and is wasted. Below 0.5mm, image surface brightness drops drastically and eye floaters become obtrusive.

Dawes' Limit (R = 116 / Aperture_mm in arcseconds) is an empirical threshold determined by William Rutter Dawes for the closest separation at which a human observer can just detect that a equal-brightness double star is elongated. The Rayleigh Criterion (R = 138 / Aperture_mm for 550nm green light) is the strict physical point where the central peak of one star's Airy disk falls onto the first dark diffraction ring of the second.

For visual observation with an eyepiece, surface brightness depends solely on the Exit Pupil (Aperture ÷ Magnification). An 8-inch f/5 Newtonian with a 5mm eyepiece (200x, 1.0mm exit pupil) and an 8-inch f/10 Schmidt-Cassegrain with a 10mm eyepiece (200x, 1.0mm exit pupil) produce the exact same visual image scale and brightness.

To a close approximation, True Field of View (in degrees of actual sky) equals the eyepiece's Apparent Field of View (AFOV) divided by Magnification: TFOV = AFOV / M. For example, an 82° wide-angle eyepiece operating at 100x shows 0.82° (49.2 arcminutes) of sky—wider than the full Moon (30 arcminutes).