Aperture Explained Part 1

Aperture Explained Part 1

This post was updated on November 19th, 2018

Have you ever wondered how to set your aperture in relation to the shutter speed (and ISO) to get a good exposure? Have you ever wondered how you could get those photos where the subject is in focus and the background is not? Have you ever wondered why photos taken with the same aperture but different lenses look different in terms of depth of field? All of this will be explained the following series of articles. There will be some math involved, but don’t give up on it just yet because it will all become clear if you stick with me. If you do not have a fancy SLR or mirrorless camera, but a compact camera, the same rules, and principles will apply. Instead of changing the aperture you will have to use a different program from your camera’s menu, and I will tell you which one. Today we will start with the definition of the Aperture and how to get good exposures. So let’s have a look.

The Definition of the Aperture

The aperture is the opening in the lens, which is responsible for part of the exposition, as it decides how much light at a given time can pass through the lens.1 It is defined as the focal length divided through the absolute diameter of the lens.

\displaystyle{Aperture}=\frac{focal\; length}{absolute\; lens\; diameter}
Figure 1: The Definition of the Aperture

So the aperture decides how far open the lens is in relation to the focal length you are using, as seen in figure 2.

But the aperture does not only have an influence on the amount of light that can pass through the lens but on the depth of field. The depth of field means the area in the photo that is sharp while its surroundings are not. So a photo of, say, a blossom, where the blossom is tack sharp and the field that surrounds the flower is out of focus, has a small depth of field.

A landscape photo where basically everything in the photo appears in focus, has a large depth of field.

To get a smaller depth of field, you need to use a wider aperture–which means a smaller aperture value. For a stunning landscape with a large depth of field, you need a narrower aperture–which means a bigger aperture value. And at this very moment you are very confused, because how can a wider aperture mean a narrower aperture value and vice versa?
Remember the definition of the aperture–the first formula I gave you?

\displaystyle{Aperture}=\frac{focal\; length}{absolute\; lens\; diameter}
Figure 5: The Definition of the Aperture

The aperture is defined as a fraction. The aperture value, which you see in your camera display, is the denominator of the fraction, while the numerator–the focal length–is 1. So if your camera display shows you an F4, you are in fact using an aperture of F/4; and if you are using F16, you are using F/16. So a lower F-number (4) means a higher F-value and vice versa, because F/4 > F/16. Or simplified: you will get more cake (1/4) if you have to share it with only four people, than if you have to share the same cake with sixteen people (1/16). (More cake = more background blur.)
For a landscape photo, you would want to have as much of the scenery in focus (less background blur) as possible–so you would therefore use a small(er) aperture, while for a photo where the subject is supposed to stand out against its surroundings (more background blur) by being the one thing in focus, you would use a narrow(er) aperture.

If you are using a compact camera for which you cannot change the aperture directly, you can achieve a small depth of field by using the macro mode, usually a menu setting with a flower icon. For a large depth of field you would use the landscape program, usually a setting with a landscape icon, and for a depth of field in between those two you would use the portrait mode.

Why are my aperture values so strange?

If you have a look at the full-stop apertures that your camera offers2, you will soon realize that those values look a little strange. Not only is one stop3 wider than 8 not 7 or 4 but 5.6…one stop narrower than 8 is not 9 or 16 (that’s actually two stops) but 11. So let us have a look why that is the case. The explanation lies in the shape of your lens. It is a cylinder, based on stacking circles on top of each other, and not a cube. So the amount of light that can pass through that “aperture-circle” in a very short timeframe–imagine super thin round slices of light–would equal the area of the circle. To calculate the area of that circle, you would use the following formula:


Figure 6: Area of the circle

Let us try an example calculation and assume that the radius of the circle is 1, which means the area of the circle would be calculated as:

\displaystyle \begin{array}{ccl}{A} & = & \pi *r^2 \; \|\scriptstyle with\; r=1 \\ \\{A} & = & \pi * 1^2 \\ \\ {A} & = & \pi \end{array}
Figure 7: Area of a circle with a radius r=1

Now what we would like is to double that area…so let’s see how large our radius needs to be for that:

\displaystyle \begin{array}{ccl} {2*A} & = & \pi * r^2 \; \|\scriptstyle with\; A=\pi \\ \\ {2* \pi} & = & \pi  * r^2 \; \|\scriptstyle divide\;through\;\pi \\ \\ 2 & = & r^2 \; \|\scriptstyle take\;squareroot\;on\;both\;sides \\ \\ \sqrt{2} & = & \sqrt{r^2} \\ \\ \sqrt{2} & = & r \\ \\ 1.41 & \approx & r \end{array}

Figure 8: Calculation of a radius of a circle in double the area

So in order to double the area of a circle you have to multiply the original radius with √2. Now let’s see what that means for our aperture-numbers, how do they change if we multiply them with √2.

Starting Aperture Next
smaller aperture (√2)
1 1.4
1.4 2
2 2.8
2.8 4
4 5.6
5.6 8
8 11
11 16
16 22
22 32
Figure 9: Aperture-numbers (full stops)

So now you know where those numbers come from 🙂 In the next article of this series, which will be published here on February 24, 2017, we will have a look into how the aperture, shutter speed, and ISO work together in creating the right exposure for your photo.

1 The shutter speed decides how long that opening exists and how long the sensor/film in your camera is exposed to the light. Back to text
2 If you are using a compact camera, you would have to look into your photo’s extended file information (exif) to see which aperture is used by which mode. This information is available for all digital cameras and can be viewed with tools like exiftool, or within, for example, the Library module of Adobe Lightroom. Back to text
3 The doubling of the area that allows light to pass through the lens is a change by plus one stop. Bisectioning of the area means a change of minus one stop. Back to text

If you enjoyed this post, you might want to have a look at the other posts of this series:

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