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#### 11.3 Numerical aperture (NA)

Numerical aperture represents the light-gathering capacity of an optical fibre. Light-gathering capacity is proportional to the acceptance angle, θ0. So, numerical aperture can be represented by the sine of acceptance angle of the fibre i.e., sin θ0.

Expression for numerical aperture (NA): Expression for numerical aperture can be obtained by applying Snell’s law at ‘O’ and at ‘B’ in Fig. 11.2. Let n1, n2 and n0 be the refractive indices of core, cladding and the surrounding medium (air), respectively. Applying Snell’s law at the point of entry of the ray [i.e., at ‘O’],

We have:

n0 sin θ0 = n1 sin θ1 _________ (11.5)

At point ‘B’ on the core-cladding interface, the angle of incidence = 90° − θ1. Applying Snell’s law ...

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