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The Aperture and the F-number

All you need to know about the camera's aperture
by Gisle Hannemyr
Published: 2010-08-31.

With reference to lenses, an aperture is a hole or an opening through in the lens' light path. The aperture is surrounded by an opaque structure (diaphragm) that can be adjusted to change the size of the aperture.

The size of the aperture opening inside the camera lens regulates amount of light that passes through onto the sensor inside the camera at the moment when the shutter curtain in camera opens during an exposure.

Large (left) and small (right) aperture. Photo: Mohylek. Used under CC BY-SA.

The illustration above shows the same lens with the diaphragm at two different settings. The photo on the left shows the diaphragm wide open, resulting in a large aperture. The photo on the right shows the diaphragm closed down, resulting in a small aperture.

The F-number

To indicate the size of the aperture, something known as an f-number is used, for example “f/2.8”. The reason it should be written like this, it that it is actually a fraction. The numerator is always the letter “f”, which refers to the focal length of the lens, and the denominator is sometimes called the f-number, and is in this case the number “2.8”.

The reason the aperture is expressed as a fraction, and not just as a number, is beause this simplifies things. If you want to know why, read the fine print.

Since the aperture is expressed as a fraction, with the f-number as denominator, a smaller f-number means a larger aperture. Lenses with large apertures (typically designated with a f-number ≤ 2.8) are sometimes referred to as “fast”. This is because such a lens is capable of delivering more light to the focal plane, allowing the photographer to a faster shutter speed, than a “slow” lens. Hence, a lens with a maximum aperture equal to f/1.4 is “faster”, and have a larger maximum aperture, than a lens with a maximum aperture equal to f/4. This means that a lens with a maximum aperture equal to f/1.4, all other things being equal, can be used in dimmer situations than one with maximum aperture equal to f/4.

The “standard” f-numbers are sometimes known as “full stops”. The list of full stops is written as a the following geometric sequence: 0.7, 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, and so on. The fractional numbers are truncated to two significant digits, but the multiplier between two adjacent numbers is actually the square root of two (1.4142…). The difference between two adjacent full stops is known as “one f-stop”. A difference of one f-stop means that the faster lens will let in twice as much light as the slower.

Looking a real lens labels, you may come across lenses with f-numbers outside the standard sequence. These are fractional stops. For example the Nikkor 85 mm f/1.8 will have a maximum aperture equal to f/1.8. This is 2/3 of a stop slower than f/1.4, and 1/3 of a stop faster than f/2.0.

Why Do We Want Fast Lenses?

Fast lenses usually cost more than slow lenses. Fast lenses with a large maximum aperture need to use larger lens elements mounted in correspondingly larger lens barrels. Larger lens elements weight more, and the lens barrel itself needs to be larger and more sturdy to keep the large lens elements in alignment. This means that fast lenses in general are more heavy to carry around, and more expensive to manufacture. They also require larger and more expensive filters.

There are, however, several advantages with using fast lenses. Having a fast lens means that you can use a faster shutter speed and/or lower ISO setting than a slow lens allow you to use. It will also give your flash a longer “reach” in dim conditions.

Standard contrast detecting autofocus sensors work better and faster when there is more light available for focusing, which means that a fast lens may give you faster and better autofocus, in particular in low light. However, a heavy construction with a lot of metal and glass to move around means that more torque is needed to drive the focus motor. If the focus motor is underpowered, you may find that a fast lens is actually slower to autofocus than a slow lens with a more lightweight design.

Which Aperture to Use

The aperture determines the depth of field. A large aperture gives a photograph a shallow depth of field, and a small aperture gives a large depth of field.

The Fine Print

In the introduction, I promised to tell you why photographers prefer to refer to use a fraction to refer to the the size of the aperture. Here is the explanation.

As we've seen, the f-number is used as a measure for aperture. The f-number is derived from the lens' real focal length. To be precise, it expresses the diameter of the entrance pupil of the lens as a fraction of the real focal length of the lens. The “f” in “f-number” is actually shorthand for focal length. For example, f/4.0 represents an entrance pupil diameter that is one-quarter of the lens' focal length. If the lens has f=100 mm, f/4.0 designates an entrance pupil diameter equal to 100/4=25 mm, and f/2.0 designates an entrance pupil diameter equal to 100/2=50 mm. So why don't we just say that the lens has a pupil size of 25 mm, or 50 mm. The latter way of doing this seems more logical, because a larger number would then indicate a larger aperture.

Well, the reason aperture is indicated by the f-number that is relative to the focal length, and not by entrance pupil diameter directly, is that the relative f-number is much more useful to the photographer than knowing the entrance pupil diameter.

The f-number will tell the photographer the amount of light that will fall on a given area of the camera's focal plane in a given period of time no matter what the focal length is. In other words, a lens with a focal length equal to 100 mm set to f/2.8 and a lens with a focal length equal to 35 mm set to f/2.8 will both use the same shutter speed and ISO setting for correct exposure. Using the f-number as a measure for exposure allows the photographer to leave the focal length out of exposure calculations and light metering.

The reason it works out like this is because, with a longer focal length, you capture a much more narrow cone of light. While the aperture “hole” is bigger with a longer focal length lens, the total amount of light captured is smaller. These two effects (more narrow cone – bigger “hole”) cancels each other exactly. This is what makes the ratio between focal length and entrance pupil diameter so useful as a metric of aperture.

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