Telescope Optics: Aperture, Focal Length, and Light Gathering
The primary function of a telescope is gathering light. Light gathering power scales with the square of the telescope aperture (objective lens or mirror diameter): \(\text{LGP} = \left( \frac{A_d}{7} \right)^2\), where \(A_d\) is the aperture in millimeters, compared to a fully dark-adapted human pupil of 7mm. A 100mm telescope gathers over 200 times more light than the human eye.
Magnification is determined by the focal length of the telescope and the eyepiece: \(\text{Magnification} = \frac{F_{\text{scope}} \times B}{F_{\text{eyepiece}}}\), where \(B\) is the Barlow lens factor (1x if none). Changing eyepieces changes magnification, but maximum useful magnification is bounded by the aperture: roughly 2x per millimeter of aperture (50x per inch). Higher magnifications simply blur the image if you exceed this limit.