NA ↔ f/# Conversion
NA = 1/(2·f/#) for objects at infinity. Relates numerical aperture to f-number.
NA = 1/(2N) = 0.1786
Half-angle of the cone = 10.29°
Airy disk diameter 2.44 λN at 550 nm = 3.76 µm
Thin-lens tangent form 1/√(1 + 4N²) = 0.1758 (1.6 % lower).
Object at infinity, lens in air. A corrected (aplanatic) lens obeys the sine condition, so its NA is exactly 1/(2N) and f/0.5 is the limit NA = 1. Focused at a finite distance, the working f-number is about (1 + |m|)·N, which lowers the image-side NA.
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
NA = 1/(2N) holds exactly for a lens that obeys the sine condition, object at infinity, in air. The thin-lens tangent form is shown for comparison; finite conjugates need the working f-number.
- Born M., Wolf E. (2019). Principles of Optics, 7th ed., ch. 4. Cambridge University Press. Abbe sine condition for aplanatic imaging. doi:10.1017/9781108769914