F-Stop Scale & Aperture Series (f/1.0 to f/22)
Direct Answer
The F-Stop Scale is a standardized geometric progression of lens focal ratios ($N = f / D$, where $f$ is focal length and $D$ is entrance pupil diameter) governed by powers of $\sqrt{2} \approx 1.4142$. Advancing one full stop (e.g. from f/2.8 to f/4.0) halves the cross-sectional area of the optical entrance pupil, cutting light transmission precisely in half (-1 EV).
Source: ISO 517:2008 (Photography — Apertures and related markings) / DIN 4522
Specs
| Mathematical Definition | F-Number N = Focal Length (f) / Entrance Pupil Diameter (D) |
| Geometric Progression Factor | Powers of √2 (~1.41421356...): √2⁰=1.0, √2¹=1.4, √2²=2.0, √2³=2.8, √2⁴=4.0, √2⁵=5.6, √2⁶=8.0, √2⁷=11.3, √2⁸=16.0, √2⁹=22.6 |
| Standard Full-Stop Scale | f/1.0 -> f/1.4 -> f/2.0 -> f/2.8 -> f/4.0 -> f/5.6 -> f/8.0 -> f/11 -> f/16 -> f/22 -> f/32 |
| Standard 1/3-Stop Increments | f/1.4, f/1.6, f/1.8, f/2.0, f/2.2, f/2.5, f/2.8, f/3.2, f/3.5, f/4.0, f/4.5, f/5.0, f/5.6, f/6.3, f/7.1, f/8.0, f/9.0, f/10, f/11, f/13, f/14, f/16 |
| Light Transmission Rule | Each full f-stop increase cuts light passing through the lens by exactly 50% (1 stop / 1 EV) |
| Diffraction Limit Physics | Airy disk diameter = 2.44 × λ × N. At f/16 and f/22 on high-res digital sensors, diffraction visibly softens fine detail |
The √2 Area Halving Principle
Because the area of a circle is $A = \pi r^2$, doubling the area of the aperture opening (to let in twice as much light) requires multiplying the radius by $\sqrt{2} \approx 1.414$. Consequently, the sequence of f-numbers ($1.0, 1.4, 2.0, 2.8, 4.0, 5.6, 8.0, 11, 16, 22$) represents the inverse diameter steps needed to double or halve light reaching the film/sensor plane.