Perfect Sight Without Glasses D. Bates.

Let’s use this result and Snell’s law to determine the entrance cone for light rays incident on the face of a clad fiber if the light is to be trapped by total internal reflection at the core-cladding interface in the fiber.

Example 3

A step-index fiber 0.0025 inch in diameter has a core index of 1.53 and a cladding index of 1.39. See drawing. Such clad fibers are used frequently in applications involving communication, sensing, and imaging.

Perfect Sight Without Glasses D. Bates.

What is the maximum acceptance angle Ɵm for a cone of light rays incident on the fiber face such that the refracted ray in the core of the fiber is incident on the cladding at the critical angle?

Solution: First find the critical angle Ɵc in the core, at the core-cladding interface. Then, from geometry, identify θr and use Snell’s law to find Ɵm.

(1) From Equation 3-3, at the core-cladding interface

Perfect Sight Without Glasses D. Bates.

(2)From right-triangle geometry, Ɵr = 90 − 65.3 = 24.7°

(3)From Snell’s law, at the fiber face,

Perfect Sight Without Glasses D. Bates.

Thus, the maximum acceptance angle is 39.7° and the acceptance cone is twice that, or 2 θm = 79.4°. The acceptance cone indicates that any light ray incident on the fiber face within the acceptance angle will undergo total internal reflection at the core-cladding face and remain trapped in the fiber as it propagates along the fiber.


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