Tapered Fibers

Tapered fibers are governed by one important relationship,
,
where diameters and angles are as shown in Figure 2-8. The angle of reflection of a light ray is equal to the angle of incidence.

Therefore, light entering the small end of a fiber becomes more collimated as the diameter increases because the reflecting surface is not parallel to the fiber axis. Collimated light entering tapered fibers at the large end, on the other hand, becomes decollimated, and if the angle of incidence exceeds the acceptance angle, it will pass through the side of the fiber. The error perhaps most frequently made by the novice is to attempt to condense an area of light that is Lambertian using a taper. As illustrated in Figure 2-9, this merely "throws" light out the sides. If the incoming light is in a small angle, the outgoing flux per unit area can be increased.

When working with a system of the "Mae West" variety (Figure 2-10), it is important to remember that the smallest diameter determines the acceptance angle of the system. This is in conformity with the relationship previously cited that governs tapered fibers.

Light entering the side of a fiber or taper can be trapped if the angle of incidence is greater than the critical angle. The stray-light cone thus produced forms the basis for one type of injection lighting (Figure 2-11).

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