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Published on March 21st, 2013 | by thappe


A Technical Walk Through Aperture Size

We talk about aperture all the time, as it is one of the key features to look at when examining a lens, worrying about exposure, or just looking for that perfectly shallow depth of field. The naming scheme can at first seem a little arbitrary, but the way we classify and actually determine f-stop is an interesting tidbit out of the optical engineering that designs our lenses.

Aperture Defined

F-stop is defined as the focal length of the lens divided through by the diameter of the aperture, and is a measure of how much light reaches the sensor in a given amount of time.

f-stop = focal length / diameter of aperture

Each full stop corresponds to the aperture opening about 1.4 times wider. Because more light enters if the opening is larger, and we know that the area of a circle is proportional to the diameter squared, each stop down means that the sensor is receiving  1/(1.4*1.4) = .5; half the light in a given amount of time. For this reason, standard f-numbers are successive multiples of the square root of two:

f , f/1.4 , f/2 , f/2.8 , f/4 ,f/5.6

And so on. An aperture has a mechanically fixed maximum value, and the longer the focal length, the larger the aperture must open maintain the same f-stop. This is why variable focal length lenses also often have variable aperture size.

An Example in Action

The Nikon 24-85mm f/3.5-4.5 is a great example of a variable focal length, variable aperture lens. The f-number can be thought of ratio of the focal length to the aperture opening. So when we say that we have an f-stop of f/3.5, that means our aperture has an opening of 24/3.5 = 6.86mm wide at the short end of the focal range. If we go out to the other end, the aperture is opened to 85/4.5 = 18.9mm. So even though less light is reaching the sensor, the aperture in fact has an area almost times as large! This simple equation shows how difficult it can actually be to create, for instance, a telephoto lens that opens up to f/2.8.

It is common practice to preach to beginners that the higher the aperture number, the smaller the opening. It seems counter-intuitive to some, but armed with this knowledge, we can  appreciate exactly how these standards arise. It also gives a fleeting insight into how vastly complex our lenses actually are, and that entire teams have come together to build the optics that we use every day.

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