Light guide and optical fiber. An ideal mechanism for guiding light is that tota

Question

Light guide and optical fiber. An ideal mechanism for guiding light is that total internal reflection at the boundary between two media of different refractive indexes. Rays are reflected repeatedly without undergoing refraction. An optical fiber is a light conduit made of two concentric glass cylinders (see Figure). The inner, called core, has a refractive index n1, and the outer, called the cladding, has a slightly smaller refractive index, n2<n1. Light rays traveling in the core are totally reflected from the cladding if their angle of incidence is greater than the critical angle c. The refractive index or air is 1.

The half-angle of cone of rays accepted by the fiber (transmitted through the fiber without undergoing refraction at the cladding) is given by:

NA=sin=(n1 ^2-n2 ^2) ^1/2
The angle is called the acceptance angle and the parameter NA=sin is known as the numerical aperture of fiber.

Question:

Calculate the NA and acceptance angle for a silica-glass fiber with n1=1.478 and n2=1.462.

Explanation / Answer

From given information, n1=1.478 , n2=1.462 and from given formula,NA = (n1^2-n2^2)^1/2 = 0.2168 and acceptance angle = arcsin(NA) = 12.526 degrees

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