numvana

Numerical Aperture Calculator (Optical Fiber)

Find an optical fiber's numerical aperture and light-acceptance cone angle from its core and cladding refractive indices, NA = √(n1² − n2²).

Numerical aperture (NA)
0.2425
Acceptance half-angle (from the fiber axis, in air)
14.033°
Full acceptance cone angle
28.067°

How it works

An optical fiber guides light by total internal reflection off the boundary between its core and its lower-index cladding — this site's Critical Angle calculator finds that boundary's own threshold angle, θc = arcsin(n2/n1). Numerical aperture restates the same core/cladding pair as a single figure describing the fiber's entire light-gathering cone as seen from outside in air: NA = √(n1² − n2²), which is algebraically n1·cos(θc) — the same physics, in the form fiber-optic datasheets actually publish.

By Snell's law at the fiber's entrance face in air, NA also equals the sine of the maximum acceptance half-angle: θmax = arcsin(NA). Any ray entering from air steeper than θmax misses total internal reflection once inside and leaks out through the cladding instead of propagating down the fiber, so NA is what ultimately limits how much light a fiber can couple in from a given source.

FAQ

Why does a bigger core/cladding index difference give a wider acceptance cone?

A bigger gap between n1 and n2 means more of the light hitting the core/cladding boundary clears the critical angle and gets totally internally reflected, which widens the range of entrance angles that still end up propagating — exactly what a larger NA = √(n1² − n2²) reports. The tradeoff is that a wider acceptance cone also typically means more modal dispersion in a multimode fiber, so real fiber designs balance NA against that cost rather than maximizing it freely.

Why is this different from the Critical Angle calculator's result?

Critical angle is measured inside the fiber, relative to the core/cladding boundary itself. Numerical aperture is measured outside, in air, relative to the fiber's own axis — it's the practical number that tells you the widest cone of external light the fiber can actually accept and still guide, which is what matters when aligning a light source to the fiber.

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