Numerical aperture

Numerical Aperture (NA) is a dimensionless number that characterizes the range of angles over which a system can accept or emit light. By incorporating the refractive index of the medium in which the lens is working, the NA has the ability to describe the light gathering power and resolution of an optical system, particularly microscopes and fiber optics.

Definition

The numerical aperture of an optical system, such as a microscope, is defined by the equation:

NA = n sin θ

where:

• n is the refractive index of the medium in which the lens is working,
• θ is the half-angle of the maximum cone of light that can enter or exit the lens.

This equation shows that the larger the NA, the greater the light gathering ability of the lens.

Applications

Microscopy

In microscopy, a larger numerical aperture will provide a higher resolution, as it allows the lens to gather more light from the object being observed. This is crucial in applications such as fluorescence microscopy and confocal microscopy, where the light emitted by the sample is often very weak.

Fiber Optics

In fiber optics, the numerical aperture is used to determine the angle at which light will be totally internally reflected within the fiber. This is important in determining the bandwidth of the fiber, as a larger NA will allow more modes of light to be propagated, increasing the bandwidth.

See Also

• Optics
• Microscopy
• Fiber Optics
• Refractive Index
• Resolution (optics)