An optical system's light-gathering capacity depends on its aperture, defined as the size of its opening (entrance pupil): the greater the aperture, the brighter the image; in addition, the image is better defined in its details (it is said to have a higher resolution). In telescopes, a greater aperture makes it possible to see fainter celestial bodies and to better resolve their structure. An aperture of 5 cm in diameter gathers about 60 times as much light as the pupil of the human eye.
The following distinctions are used:
Linear aperture (when one refers to aperture in generic terms, this is the usual meaning): the useful diameter of the opening of the optical system. In a refracting telescope, denotes the diameter of the objective or a fraction of it; in a reflecting telescope, usually refers to the diameter of the primary mirror.
Focal ratio (or relative aperture or f-number, f/N): ratio of the focal length to the linear aperture. By definition, a smaller focal ratio means a greater luminosity. On a camera lens, for example, the marking f/2 indicates that the linear aperture is equal to one-half the focal length.
Numerical aperture (NA): characterizes the maximum light-gathering angle, measured with respect to the optical axis. Mathematically defined by the angle's trigonometric sine function, multiplied by the refractive index of the medium in front of the objective. When the medium is air (whose refractive index is approximately 1), the numerical aperture does not exceed 1; the closer it is to 1, the brighter the image and the greater its resolution. Numerical aperture is generally used for microscope objectives; for example, the notation NA 0.5 means that the largest light-gathering cone extends by ± 30° around the optical axis (sin 30° = 0.5).