Numerical aperture is a dimensionless number that characterizes the range of angles over which an optical system can accept or emit light. It is a measure of the ability of an optical system, such as a microscope objective or a fiber optic cable, to gather light and resolve fine specimen detail. Numerical aperture is defined as the product of the refractive index of the beam from which the light input is received and the sine of the maximum ray angle against the axis, for which light can be transmitted through the system based on purely geometric considerations.

In microscopy, numerical aperture is used to describe the acceptance cone of an objective, which determines its light-gathering ability and resolution. Lenses with larger numerical apertures collect more light and generally provide a brighter image, but they also provide shallower depth of field. In fiber optics, numerical aperture describes the range of angles within which light that is incident on the fiber will be transmitted along it.

Numerical aperture is not typically used in photography, where the angular aperture of a lens is expressed by the f-number. The numerical aperture of an objective is difficult to measure directly, except in limiting cases with rather large apertures and negligible diffraction effects.

In summary, numerical aperture is a measure of the range of angles over which an optical system can accept or emit light. It is commonly used in microscopy to describe the acceptance cone of an objective and in fiber optics to describe the range of angles within which light can be transmitted along a fiber.