Telescope magnification, exit pupil and f-ratio
How focal length, eyepiece, and aperture combine to set magnification, image brightness, and the useful power limit of a telescope.
Where magnification comes from
Magnification is not built into a telescope; it is set by the eyepiece you slot in. The figure equals the telescope focal length divided by the eyepiece focal length, both in millimetres. A 1000 mm scope reaches 100x with a 10 mm eyepiece and only 40x with a 25 mm one. This is why observers carry several eyepieces: each one is a different power for the same tube. Doubling the eyepiece focal length halves the magnification, and a Barlow lens multiplies the effective scope focal length to squeeze out more.
The aperture sets the ceiling
The diameter of the main lens or mirror, the aperture, decides how much light and detail the telescope can collect. A widely used rule puts the maximum useful magnification at about 2 times the aperture in millimetres, so a 150 mm scope caps near 300x. Beyond that point extra power just enlarges a fixed pool of detail, and the view dims and softens rather than sharpening. Aperture also drives resolving power, so a larger objective splits tighter double stars and shows finer planetary markings than any eyepiece swap can.
Exit pupil and brightness
The exit pupil is the narrow shaft of light that exits the eyepiece and enters your eye, and it equals the aperture divided by the current magnification. Low power produces a fat exit pupil and a bright image, while high power narrows it and dims the view. A dark adapted human pupil opens to roughly 7 mm, so an exit pupil wider than that spills light around your iris and is wasted. At the other end, exit pupils under about 0.5 mm start to reveal floaters and diffraction, which is one more reason very high powers disappoint.
Focal ratio and what fast means
The focal ratio, written f/ followed by a number, is the focal length divided by the aperture. An f/5 scope is fast and floods a wide field with light, favouring nebulae and star fields, while an f/10 scope is slow with a narrower, higher contrast field suited to the Moon and planets. Focal ratio does not change how much total light the aperture gathers, but it does set the image scale and the eyepiece focal lengths you need to reach a given power. It is a fixed property of the optics, unlike magnification, which you change with each eyepiece.