A factor in determining how much light a fiber collects is its acceptance angle, the range of angles over which a light ray can enter the fiber and be trapped in its core. The full-acceptance angle is the range of angles at which light is trapped; it extends both above and below the axis of the fiber. The half-acceptance angle is the angle measured from the fiber axis to the edge of the cone of light rays trapped in the core; it is shown in Figure below.

*Numerical aperture (NA) measures the fiber’s acceptance angle.

The standard measure of acceptance angle is the numerical aperture, NA, which is the sine of the half-acceptance angle, 0, for reasonably small angles. For a step-index fiber, it is defined as

where is the core index and n1 is the cladding index. A typical value for step-index single-mode fiber is around 0.14.

Numerical aperture is not calculated the same way in graded-index fibers; strictly speaking it varies across the core with the refractive index. However, you can measure numerical aperture by monitoring the divergence angle of light leaving a fiber core. As shown in Figure below

The light emerging from a multimode fiber spreads over an angle equal to its acceptance angle.
For practical measurements, care must be taken to eliminate modes guided in the cladding, and the edge of the beam is defined as the angle where intensity drops to 5% that in the center. NA can be calculated easily from the acceptance angle. Typical NA values are 0.20 for 50/125 graded-index fiber, and about 0.28 for 62.5/125 graded-index fiber.
Core diameter does not enter into the NA equation, but light rays must enter the core as well as fall within the acceptance angle to be guided in the core. Large core size and large NA do not have to go together, but in practice larger-core fibers tend to have larger core-cladding index differences and thus larger NAs. For example, step-index multimode fibers typically have NAs of at least 0.3, more than twice the value for single-mode step-index fibers.
The numerical aperture of single-mode fibers is defined by the same equation as for multimode fibers, but light does not spread out from them in the same way. (They carry only a single mode, and their cores are so small that another wave effect called diffraction controls how light spreads out from the end.) NA generally is not as important for single mode fibers as it is for multimode fibers.