Numerical Aperture⚠ unverified
Physics / Optics · Compute the numerical aperture of an optical fiber
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| n | n | — | 1.0 | Refractive index of the surrounding medium (dimensionless) |
| theta | θ | — | 1.0 | Half-angle of the maximum acceptance cone, in degrees |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | NA | — | Numerical aperture (dimensionless) |
The science & history
Understanding the Parameters
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$n\sin\theta$ — cannot exceed $n$; for fibers $\mathrm{NA} = \sqrt{n_{\mathrm{core}}^{2}-n_{\mathrm{clad}}^{2}}$ is an alternate definition.
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NA — microscope objectives quote NA; resolution $\sim \lambda/(2\,\mathrm{NA})$.
Derivation (Approaching a Proof)
Definition of NA from the marginal ray angle in medium $n$. Diffraction theory links NA to the maximum spatial frequency collected by the system.
History
Abbe’s work on resolution made NA the key microscope specification.
Related Concepts: Rayleigh Criterion, Critical Angle, Etendue, Snell's Law refraction angle
Notes: Registry calculator numerical-aperture (unverified). $\theta$ in radians.