Engineering Physics

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 ...