Science calculator
Numerical aperture.
Relate numerical aperture to refractive index and acceptance half-angle, or estimate its paraxial air-space f-number equivalent.
- Half-angle in the selected medium
- —
- Full cone in the selected medium
- —
- Paraxial air f-number
- —
- NA numerical aperture · n refractive index in the object or launch space · θ marginal-ray half-angle · N f-number
Assumptions
- θ is the half-angle from the optical axis to the marginal accepted or collected ray.
- The refractive index is uniform in the launch or object space and NA cannot exceed n.
- The f-number relationship NA ≈ 1/(2N) is a paraxial air-space approximation; it becomes inaccurate at high NA.
- Acceptance angle describes geometric access for coupling, not coupling efficiency, mode overlap, Fresnel loss or alignment tolerance.
How it works
Numerical aperture combines the refractive index with the angular size of the accepted light cone. A larger NA accepts steeper rays and can collect more spatial information.
For a fibre in air, the acceptance half-angle indicates which launch directions can be guided in the ideal ray model. Efficient coupling still requires the beam position, waist and mode shape to match.
Leave one field blank in the chosen relationship. The f-number mode is intended for low-to-moderate NA comparisons, not precision high-NA objective design.
- Free
- No ads
- No tracking
- No account
- Works offline once loaded
From the maker of Ans — a scientific calculator you can own. Same idea: a proper instrument, nothing in the way.