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# Apertures and f-stops

Lens aperture settings are commonly knows as f-stops

. The letter f

is an abbreviation of the term focal-ratio

, which describes the ratio of a lens's focal length to the diameter of the light entrance pupil (more commonly called the aperture).

The standard sequence of f-stops is:

f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22.

Here's the maths for a 50mm lens - to show how the stops got their names.

f-stop | Diameter(mm) | Focal-ratiolength: aperture |

f/1.4 | 35.7 | 1:1.4 |

f/2.0 | 25.0 | 1:2 |

f/2.8 | 17.9 | 1:2.8 |

f/4 | 12.5 | 1:4 |

f/5.6 | 8.9 | 1:5.6 |

f/8 | 6.3 | 1:8 |

f/11 | 4.5 | 1:11 |

f/16 | 3.1 | 1:16 |

f/22 | 2.3 | 1.22 |

This ratio is commonly detailed on the bezel around the front element of most lenses (e.g. 50mm 1:1.8, or sometimes 50mm f:1.8).

On this scale, an f/1.4 setting is the largest aperture, while f/22 is the smallest, and each f-stop in the sequence is half the size of its neighbour to the left, and twice the size of its neighbour to the right. In other words, f/5.6 permits the passage of twice as much light as f/8, but only half the light of f/4.

Low f-stop numbers represent larger apertures, and higher f-stop numbers indicate smaller apertures because the f-stop is a ratio comparing the size of the aperture and the focal length of the lens; i.e. a bigger number represents a larger difference.

Here's a bit more maths to prove this relationship: you just need to follow the logic. Let's start with f/2 on a 50mm lens. This f-stop has a diameter size that is half the focal length of the lens: that is 25mm.

The area of a circle is calculated using the formula - πr^{2}.

Expressed in words, this is "Pi" (the common name of the π symbol, which represents 22 ÷ 7) times the radius (r) squared, which is another of way of saying radius x radius. You will no doubt remember that the radius of a circle is half the size of its diameter.

The calculation of the area of f/2 for a 50mm lens is therefore: (^{22}/_{7}) x (12.5 x 12.5).

Repeating this calculation for each f-stop produces the following results:

f-stop | Diameter(mm) | Areamm ^{2} |

f/1.4 | 35.7 | 1,002 |

f/2.0 | 25.0 | 491 |

f/2.8 | 17.9 | 250 |

f/4 | 12.5 | 123 |

f/5.6 | 8.9 | 63 |

f/8 | 6.3 | 31 |

f/11 | 4.5 | 16 |

f/16 | 3.1 | 8 |

f/22 | 2.3 | 4 |

What you should see in this table is proof that the area of each f-stop is double/half the size of each neighbour (results shown to the nearest whole number).

The point of all this dull maths is three-fold:

- it proves the claimed relationship made at the beginning of this article,
- it explains why lenses use such an odd sequence of numbers to name f-stops,
- and it equips us to understand the in-between apertures, such as f/1.8, and other idiosyncrasies of the naming system.

If 35mm film photography is your thing, you will have inevitably encountered some f-stops that don't fit the opening sequence: f/1.7, f/1.8, f/1.9, f/3.5 and f/4.5 are some of the most common ones.

• f/1.7 is one-half-stop larger than f/2.

• f/1.8 is one-third-stop larger than f/2.

• f/1.9 is one-quarter-stop larger than f/2. • f/3.5 is one-third-stop larger than f/4. • f/4.5 is one-third-stop smaller than f/4.An understanding of these in-between f-stops has a further day-to-day application: setting a lens aperture in-between f-stops. Most lenses have an aperture ring that is click stopped

. That is to say, rather than visually aligning an aperture setting, the ring clicks into place when alignment is correct. Some lenses also have clicked half-stops. Others have no click stops at all. Either way, when half-stops are set visually, they fall about 1/3rd of the distance from the wider aperture alignment (take my word for it, but you can do the maths is you wish).

With different focal length lenses, the standard apertures will be physically different sizes (e.g. f/2 on a 100mm lens will have a diameter of 50mm), but fortunately the expression of f-stops as ratios means that, say f/2, will always permits the same level of light to pass whether it's f/2 on a 50mm lens, or a 100mm lens, or any other focal length (i.e. 50mm focal length = 25mm aperture diameter > a ratio of 1:2. 100mm focal length = 50mm aperture diameter > a ratio of 1:2).

Most zoom lenses have a variable aperture

. The lens has two f

numbers, i.e. f/3.5 to f/5.6. This means your widest aperture (lower number) changes at different focal lengths, and these two numbers reflect changes to the maximum aperture relative to the focal length setting in use. For example - imagine a 50mm to 100mm lens with an f/2 aperture. At the 50mm focal length, the aperture diameter is 25mm - a ratio of 1:2. At the 100mm focal length, that 25mm aperture diameter will be in the ratio of 1:4, which is f/4.

Expensive zoom lenses may have a constant aperture

. Briefly, this is accomplished by placing moving (focal length altering) lens elements behind the diaphragm, so that the focal length is altered without changing the effective aperture.

Other pages in this series at Camera Portraits

Analog/Analogue/Argentic? ... or we could just call it film photography!