Why are only certain aperture values (i.e. 1.4, 2.0, 2.8, 4, 5.6, 8, 11, 16, 22) used? Is there a reason we can't use anything other than those values - for example, 1.8 or 2.7?
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1If you have comments or additional questions, use the "add a comment" feature, don't add another answer. All cameras allow you to change the aperture, it's part of the core functionality. – Michael Borgwardt Oct 23 '15 at 09:14
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@MichaelBorgwardt my compact camera doesn't allow me to change the aperture in any meaningful way - the only controls are ISO and exposure compensation. – Philip Kendall Oct 23 '15 at 09:46
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Will do mr. Michael – Vasu G Varma Oct 23 '15 at 10:26
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The f-number represents a ratio between the focal length and the diameter of the entrance pupil, which makes it a) easy to calculate for a given lens and b) very useful for usage independant of specific lenses because its effect is independant of the focal length.
As for why the specific "f-stop" number series you cite is used: these aperture values have the important property that each one lets in half as much light as the previous one. This makes them very easy to work with when you vary your exposure settings: if you double the shutter time and want to keep overall exposure the same, just step down the aperture one f-stop to compensate.
But it's not true that only these numbers can be used: in fact, most cameras nowadays allow you to change aperture settings in at least "half-stop" steps, many also one-third stops, for finer control.
Michael Borgwardt
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In fact, Previous analogic cameras too. You simply did not waited to hear the "click" :o) – Rafael Oct 28 '15 at 05:16
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It's perhaps worth mentioning also that some lenses allow for a continuous adjustment of the diaphragm, e.g. most of the Soviet Jupiters. – Kahovius May 02 '19 at 11:48
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Historically is was only necessary to adjust the exposure with an accuracy of one (1) f/stop. The f/stop sequences is based on the geometry of circles. If we multiply the diameter of any circle by the square root of 2 (1.414), we calculate a revised circle with twice the surface area. Now a circle with twice the surface area allows twice as much light to transverse the lens. Thus the sequence 1 – 1.4 – 2 – 2.8 – 4 – 5.6 – 8 – 11 – 16 – 22. Note: each number going right is its neighbor on the left multiplied by 1.4 and then rounded. This number set doubles or halves the surface area thus the working diameter (aperture) increment is a 2X change. The f/number set is a ratio that takes into account the two key factors of working diameter (aperture) and focal length. The system takes the chaos away. Any lens functioning at the same f/number as another, delivers the same image brightness at the focal plane.
In time photo materials with less latitude (slide film) it became necessary. Now the industry needed a f/number set in ½ f/number increments. This time we use the fourth root of 2, This number set is 1 – 1,2- 1.4 – 1.7 – 2 – 2.4 – 2.8 – 3.5 – 4 etc. The multiplier is 1.19.
We can go to an increment of 1/3 f/stop. This is the sixth root of 2 = 1.12. The sequence is 1 – 1.1 – 1.3 – 1.4 – 1.6 – 1.4 – 1.6 – 1.8 – 2 – 2.2 -2.5 – 2.8 etc.
In the early days, German cameras labeled staring at f/4.5. The Sequence was 4.5 – 6.3 – 9 – 12.5 – 18 – 25. At the same time American camera makers tried a system 1 – 2 – 4 – 8 – 16 – 32 – 64. In this system, 1 = f/4 – 2 = f/5.6 – 4 = f/8 etc.
Alan Marcus
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"Any lens functioning at the same f/number as another, delivers the same image brightness at the focal plane." Unfortunately, that isn't true. See "transmission", http://photo.stackexchange.com/a/21943/32110 – ths Oct 27 '15 at 17:58
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1The error is for the most part to small to matter except in rare instances. The sprit of the f/stop method remains intact. – Alan Marcus Oct 27 '15 at 21:32