How does the numerical aperture (NA) of an optical fiber affect its light-gathering ability?

The numerical aperture (NA) of an optical fiber directly determines its light-gathering ability, which is the fiber's capacity to accept and propagate light. The NA is a dimensionless number that quantifies the range of angles over which the fiber can accept light. A higher NA indicates a greater light-gathering ability. The NA is defined as the sine of the maximum acceptance angle, which is the largest angle at which light can enter the fiber and still be guided by total internal reflection. The NA is related to the refractive indices of the fib....