Numerical Aperture
The previous sections of this chapter have discussed the process of light travelling through an optical fiber. This section will discuss the requirements for transmitting into an optical fiber. It is a requirement that for light to successfully travel down an optical fiber it must enter the fiber and reflect off the cladding at greater than the critical angle. Due to the refractive changes to the direction of the light as it enters the core of a fiber there is a limit to the angle at which the light can enter the core for it to successfully propagate down the optic fiber. Any light striking the cladding at less than the critical angle will go straight through into the cladding and be lost. This is illustrated in Figure 5.
Figure 5. Light
Entering the Core of a Fiber
Since the fiber is cylindrical there will be a geometrical cone at the entrance to the fiber. For light entering the core within this cone all the light rays will strike the cladding at greater than the critical angle and will therefore allow successful transmission down the fiber. This is referred to as the 'Acceptance Cone' and is illustrated in Figure 6.
Figure 6. Cone
of Acceptance of an Optic Fiber
The half angle (
)
of this acceptance cone is referred to as the 'Acceptance Angle'.
The value of the acceptance angle will depend on the refractive indices of the core, cladding and air (air having a
refractive index of 1) or whatever material the
source of light is. A light ray entering the core at an angle greater than 
will disperse into the cladding. A light
ray coming in at an angle of exactly 
will strike the core/cladding interface at
angle 
(critical) and will leave parallel to the interface.
A measurement is used to specify the light collecting ability of a fiber. This is referred to as the 'Numerical Aperture' (NA).
NA is the SIN of the acceptance angle,
that is:
NA = SIN ()