By Zencalcy Editorial TeamLast reviewed About us
Numerical aperture measures how wide a cone of light an optical system can accept or deliver. A high NA collects more light and resolves finer detail, but it comes with a shorter working distance and tighter alignment tolerances.
Light-gathering cone of a fibre or microscope objective.
NA = n sin θ NA ≈ 1 / (2N)
n is the refractive index of the medium, θ the half-angle of the acceptance cone and N the f-number of a lens in air. The f-number form is the paraxial approximation.
| Symbol | Meaning |
|---|---|
| NA | Numerical aperture, dimensionless. |
| n | Refractive index of the medium. |
| θ | Half-angle of the acceptance cone. |
| N | f-number, the focal ratio. |
NA = 1.5 × sin 30° = 0.75. The same NA in air would accept a 48.6° half-angle, which is why immersion objectives reach higher NA.
Continue with the Optical Path Length Calculator, Prism Deviation Calculator, or the Refractive Index Calculator — or browse more optics and light tools and all physics calculators.
Immersion oil has an index close to glass, so the cone does not refract at the sample. That allows a wider angle and a numerical aperture above 1.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026