Aperture Explained Part 3

Aperture Explained Part 3

 

In the first two articles of this series we had a look into the definition of the aperture, how it influenced the depth of field1 and how it–combined with the shutter speed and the ISO–built the exposure triangle. This last article will look into how the aperture together with the focal length has an influence on the depth of field.

The Relation between Aperture and Focal Length

Do you remember the definition of the aperture from the first article of this series? It was:

\displaystyle{Aperture}=\frac{focal\; length}{absolute\; lens\; diameter}

Figure 1: The Definition of the Aperture

It states that there is a relation between aperture and focal length.

If you take two photos of the same object, both with the same focus point, distance between object and camera, aperture, ISO, and shutter speed you could still change your depth of field by changing the focal length of your lens–either by changing to another lens, or by using the zoom-ring if your lens is a zoom lens.
The smallest depth of field is created by using the longest possible focal length with the widest possible aperture. The largest depth of field is created by using a short focal length in combination with a narrow aperture.
But why is that the case?
What happens to the absolute lens diameter if we use a fixed aperture of F/4.5 and different values for the focal length?

Let us first calculate the absolute lens diameter for a focal length of 200mm with an aperture of F/4.5 :

\displaystyle \begin{array} {ccl} Aperture & = & \frac{focal\; length}{absolute\; lens\; diameter} \\ \\ \frac{1}{4.5} & = & \frac{200}{absolute\; lens\; diameter}\;\;\|\scriptstyle{*4.5} \\ \\1 & = & \frac{200*4.5}{absolute\; lens\; diameter} \\ \\ 1 & = & \frac{900}{absolute\; lens\; diameter}\;\;\|\scriptstyle {*absolute\; lens\; diameter}\\ \\absolute\; lens\; diameter & = & 900\end{array}

Figure 2: Absolute lens diameter for a 200mm lens at F/4.5

What would happen to the absolute diameter of the lens if the focal length was only 100mm and the aperture stayed at F/4.5?

\displaystyle \begin{array} {ccl} Aperture & = & \frac{focal\; length}{absolute\; lens\; diameter}\\ \\ \frac{1}{4.5} & = & \frac{100}{absolute\; lens\; diameter}\;\;\|\scriptstyle{*4.5} \\ \\ 1 & = & \frac{100*4.5}{absolute\; lens\; diameter} \\ \\1 & = & \frac{450}{absolute\; lens\; diameter}\;\;\|\scriptstyle {*absolute\; lens\; diameter} \\ \\ absolute\; lens\; diameter & = & 450 \end{array}

Figure 3: Absolute lens diameter for a 100mm lens at F/4.5

So the absolute lens diameter gets smaller with a smaller focal length and a given aperture. But then…this looks like the depth of field should get smaller with a smaller focal length and not wider?
But the depth of field and the absolute lens diameter are actually anti-proportional to each other, so a wider depth of field is reached by a narrower absolute lens diameter, and a wider absolute lens diameter causes a smaller depth of field.

Depth of field Aperture Focal length
smaller wider longer
wider narrower shorter
Figure 4: Depth of field depending on lens diameter

So that means if we changed our lens from a 100mm to a 200mm lens and used the same aperture with both, our depth of field would get smaller. To counter-act on the smaller depth of field caused by a longer focal length we would use a narrower aperture. Of course, if we need to take a photo with a smaller depth of field on a shorter focal length we would use a wider aperture. A very rough, but still good starting point, is to use a quarter of the original aperture (-4 stops) with double the focal length to get a similar depth of field experience.2
If you would like to see those numbers for different focal lengths and apertures there is a variety of depth of field calculators online, the one I found helpful was this one by DOFMaster. You could, of course, start calculating the depth of field yourself by using DOFMaster’s formulas

For a brief overview I have collected3 the depth of field’s near and far limit as well as the total for a selection of focal lengths and apertures–with an anticipated subject distance of 10m–in the table below.

Aperture 25mm 50mm 100mm 200mm
F/4

Dof near: 4.39m
Dof far: ∞
Dof tot: ∞

Dof near: 7.58m
Dof far: 14.7m
Dof tot: 7.09m

Dof near: 9.27m
Dof far: 10.09m
Dof tot: 1.59m

Dof near: 9.81m
Dof far: 10.2m
Dof tot: 0.39m

F/8

Dof near: 2.81m
Dof far: ∞
Dof tot: ∞

Dof near: 6.11m
Dof far: 27.5m
Dof tot: 21.4m

Dof near: 8.63m
Dof far: 11.9m
Dof tot: 3.25m

Dof near: 9.62m
Dof far: 10.4m
Dof tot: 0.79m

F/16

Dof near: 1.64m
Dof far: ∞
Dof tot: ∞

Dof near: 4.4m
Dof far: ∞
Dof tot: ∞

Dof near: 7.59m
Dof far: 14.6m
Dof tot: 7.04m

Dof near: 9.27m
Dof far: 10.9m
Dof tot: 1.58m

F/22

Dof near: 1.22m
Dof far: ∞
Dof tot: ∞

Dof near: 3.57m
Dof far: ∞
Dof tot: ∞

Dof near: 6.91m
Dof far: 18.1m
Dof tot: 11.2m

Dof near: 9m
Dof far: 11.2m
Dof tot: 2.25m

F/32

Dof near: 0.89m
Dof far: ∞
Dof tot: ∞

Dof near: 2.82m
Dof far: ∞
Dof tot: ∞

Dof near: 6.12m
Dof far: 27.3m
Dof tot: 21.2m

Dof near: 8.64m
Dof far: 11.9m
Dof tot: 3.22m

Figure 5: The change of Depth of field (Dof) depending on focal length and aperture

Let us have a look at some example photos, that are all taken from the same distance but with a different focal length setting:

For better comparison the 55mm focal length photo and the 97.5mm focal length photo both with an aperture of F/8 next to each other

55mm F/8 97.5mm F/8
Focal length blurry on f/8
97.5mm F/8 (roughly double the focal length and 2 stops narrower aperture)
Figure 9: Comparison 55mm and 97.5 mm focal length with aperture F/8

And the 55mm focal length photo with an aperture of F/4 and the 97.5mm focal length photo with an aperture of F/8 next to each other:

55mm F/4 97.5mm F/8
55mm F/4 97.5mm F/8 (roughly double the focal length and 2 stops narrower aperture)
Figure 10: Comparison focal length 55mm at F/4 to 97.5mm at F/8

As you can clearly recognize the fence pole right before the one with the pear is slightly blurry in these last two photos, while it was tack-sharp for the 55mm F/8 photo above.

Though we don’t have any 97.5mm F/32 photos to compare with the 55mm F/8 photo, we can clearly see that with a narrower aperture that the 97.5mm photo is getting closer to the depth of field of the 55mm F/8 photo.

All of these photos were taken from a distance, but of course, the same rules apply when you are taking close-up macro shots, even though the depth of field in these cases gets even smaller. Why is that?
Generally the parts of the photo that are in focus are 1/3 ahead of the focal point and 2/3 behind the focal point. So if you choose to focus on 180cm–with a depth of field of 180cm–an area between 120cm and 300cm should be in focus. But when you are focusing on something 18cm away from you the area in focus–for the same focal length and aperture as in the previous example–is between 12cm and 30cm–instead of being 180cm long like in the first example it is now only 18cm long. Go even closer and it shrinks even more…
So in order to get the entire Iguana sharp for a focal length of 100mm in the following photo I had to use an aperture of F/29:

For a similar short focal distance–the distance between the sensor/film in your camera and your focal point on your subject–and an aperture of F/2.8 the result would look like this for a 100mm focal length:

And last but not least for a short focal distance and an aperture of F/8 the results for a focal length of 100mm look for example like this:

Yes, this all is confusing, to say the least, but try it with your camera for a few photos and it will start making sense.

On Friday, April 21, 2017, I am going to present you with some exercises fitting the content of this article series. These should allow you to gain a deeper understanding of the aperture.

1 The depth of field is the area in front and behind the subject that appears in focus in the photograph. Back to text
2 This is not an exact value, but it works well enough 🙂 Back to text
3 The calculations are done by: DOFMaster. Back to text

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

5 thoughts on “Aperture Explained Part 3

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    1. Thank you for your nice comment.
      Could you explain what you would like to know in regards to that post from the past you are referring to? I can’t quite follow your chain of thoughts. Thank you.

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