Telescope Magnification by Eyepiece & Focal Length

Magnification is the ratio between the angle an object subtends when viewed through the instrument and the angle it subtends to the unaided eye. For a telescope focused at infinity that ratio reduces to the objective focal length divided by the eyepiece focal length. Because it is a ratio of focal lengths, magnification is the one major parameter an observer can change at will by swapping eyepieces, while aperture and focal ratio are fixed by the hardware. A 1200mm f/6 Newtonian gives 48x with a 25mm eyepiece and 240x with a 5mm. Exit pupil, aperture divided by magnification, is the complementary quantity and falls from 4.17mm to 0.83mm across that same pair, which is why the low-power view looks bright and the high-power view looks dim. Useful power is bounded at both ends. The upper bound near 2x the aperture in millimetres, equivalently 50x per inch, comes from diffraction: at that power the Airy disk, whose angular diameter is about 2.44 times the wavelength divided by the aperture, has been enlarged to roughly the resolution limit of the eye, and further magnification only spreads a blur. This is called empty magnification. Atmospheric seeing usually intervenes first, capping practical power near 200x to 300x on average nights even for large instruments. The lower bound comes from exit pupil: below roughly aperture divided by 7, the emerging light cone overfills a dark-adapted pupil, wasting aperture and, in reflectors, making the secondary mirror shadow visible.

Magnification was the first telescope specification anyone quoted. Galileo Galilei built instruments reaching roughly 20 to 30 times during 1609 and 1610, sufficient to resolve lunar mountains and the four large satellites of Jupiter reported in Sidereus Nuncius in 1610. His Dutch-form design used a concave eyepiece and delivered a notoriously narrow field. Johannes Kepler described the alternative in Dioptrice in 1611, substituting a convex eyepiece for an inverted but far wider and higher-power view. That astronomical arrangement is what the focal-length ratio formula describes and what practically every telescope built since has used. The seventeenth-century pursuit of power ran straight into chromatic aberration, and since the defect weakens as focal ratio grows, observers such as Johannes Hevelius and Christiaan Huygens built extraordinarily long instruments, including tubeless aerial telescopes tens of metres in length, to reach a few hundred magnifications. Achromatic doublets, patented by John Dollond in 1758 following earlier work by Chester Moore Hall, made high power practical in short tubes. The guideline that useful power stops near 50x per inch of aperture emerged later from diffraction theory and accumulated observing experience, and became a fixture of amateur guides largely as a corrective: mass-market telescopes were, and still are, advertised by inflated claims such as 600x on a 60mm objective, where the genuine ceiling is about 120x.