Technical minutia, but I found that I felt a lot more confident once I understood this: The reason f-number is written like so is because it's not a measure of actual aperture diameter but is instead the ratio of aperture diameter to focal length. Specifically, (f-number) = (focal length)/(aperture diameter), or:<p><pre><code> N = f/A
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equivalent to,<p><pre><code> A = f/N
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Hence the format <i>f</i>/N, since you (theoretically) use f-number to calculate actual aperture diameter when given a specific focal length. That aperture is in the denominator also explains why smaller f-numbers are brighter.<p><i>Why those weird numbers in particular?</i> As in the article, a 'stop' is a doubling or halving of the brightness (technically, 'illuminance') of the image produced by the lens. Since the amount of light that passes through an aperture is proportional to its area, which is in turn proportional to the square of its diameter, one stop corresponds to a sqrt(2) ~ 1.4 ratio between two aperture diameters. Hence, the standard scale of full f-stops is the powers of two and their geometric means:<p><pre><code> f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, f/32, f/45, f/64
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The full stop scale in the article has some errors: f/1.8 instead of f/1.4, a typo for f/4/0, and a lack of f/45 (though f/1.8 is the stop below f/2 in the finer 1/3- and 1/4-stop scales):<p><pre><code> f/1.8, f/2.8, f/4/0, f/5.6, f/8.0, f/11, f/16, f/22, f/32, f/64
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<i>But why measure image brightness using f-number instead of aperture diameter directly?</i> Because brightness also depends on focal length: Doubling the focal length of a lens doubles the size of the image of an object seen through it. Since the light from the object is spread out over four times the area, the image brightness is quartered. This means lenses with equal aperture diameters and different focal lengths will not have the same exposure. (below edited, I confused myself at first!) But photographers would rather not have to consider focal length when choosing an aperture for proper exposure. Designing lenses such that their aperture controls are labelled with f-number enables this, since actual aperture diameter then scales automatically with focal length to cancel out its effects on exposure.