The term f-stop is a ratio.  It has no dimensions.  You don’t measure an f-stop in meters, inches, kilograms or even degrees Fahrenheit.  An f-stop is the ratio of two distances.  It’s the ratio of the focal length of a lens to its diameter.  In figure 1, the f-stop is f/d where f is the focal length and d is the diameter.

The f-stop of this lens is f/d

Why do we care about a lens’s f-stop?

Before we answer this, let’s review how cameras work.  A camera uses a lens to focus light on one side of the lens (the outside) onto a film or sensor on the other side of the lens (the inside of the camera).  The more light that falls on the film or sensor, the brighter the image will be.  Most films or sensors need a certain minimum amount of light in order to take a good picture (one that’s not too dark).  If there’s too much light, though, the picture will be too bright.

Now, in photography terminology, the size of the hole that light passes through is known as the aperture.  As a simplification, you can think of this as the effective diameter of the lens.    In other words, d is the diameter of the aperture.  The bigger the aperture, the more light will pass through, and the brighter the picture will be.  So you can see why d is important.  The bigger the aperture, the less time you need to pass a sufficient amount of light for a good picture.

You can use the bucket analogy: think of the lens as a hole in the bottom of a bucket. If you want to drain the bucketful of water through that hole, the bigger the hole, the less time you need for the bucket to drain.

Another measurement of a lens that’s important is f, the focal length.  Lenses with a small focal length are called wide angle lenses — they allow light from a wider angle to pass through the lens and onto the film (or sensor).  Lenses with a large focal length are called telephoto lenses — they allow a smaller cone of light into the lens, but the benefit is that picture is bigger (you can see things far away clearly).

So now we can revisit why we should care about a lens’s f-stop. The f-stop is defined as f/d, so if you have two lenses with the same focal length, the one with the smaller f-stop will have a larger aperture – it’s diameter will be larger and it will allow more light through.

Why are advertised f-stops numbered so strangely?

Lenses are circular. The apertures through which light travels are circular. The amount of light that can pass though the lens depends on the area of the circle that defines the aperture. The area of a circle is πr² where r is the radius, or half of the diameter.

F-stops are defined so that every consecutive f-stop either doubles or halves the amount of light entering the lens. To get area to double or halve at every adjacent f-stop, the ratio of adjacent f-stops need to be the square root of 2 (1.414).  A more detailed explanation can be found here.

Why don’t we just use the diameter?

The definition of the f-stop is a way to have different lens manufacturers agree on a standard.  Two lenses with an f-stop of 1.4 means the same amount of light can enter the lens, regardless of the focal length of the lens.  This also allows for lightmeters to display their results without having to know what lens you’re using to take a picture.

References

• Focal length and F-Stop Explanation
• A Tedious Explanation of the F/Stop
• Plural Posessive of Lens – TheFreeDictionary.com

Licenses

• Figure 1was adapted from
  http://en.wikipedia.org/wiki/File:Focal-length.svg and is licensed under
  the Creative Commons Attribution ShareAlike 3.0 License.

Have you ever noticed that people can run faster on flat ground than on sand or water?  It’s the same way with light.  Light travels faster in air than in glass.

When light travels through air it moves at roughly the ‘speed of light.’ When light hits a glass surface, it can’t move as fast, and slows down. If the light hits the glass at an angle, something very strange happens. It bends a bit.

Imagine a car driving off an asphalt surface onto a sandy pit at an angle. As shown in Figure 1 below, the right wheel gets onto the sand first, and slows down a little bit.  Meanwhile, the left wheel is still moving at the original speed.  This causes the car to turn slightly towards the right.

Figure 1

Light behaves the same way – depending on the angle at which it hits the glass, it bends a little bit or a lot when it starts moving in the glass. Similarly, light also bends when it comes out of glass into the air.

Figure 2

Now, a lens is just a specially shaped piece of glass.  A convex lens is one that bulges outward.  When a beam of light hits a convex lens ‘head on’ (parallel to the principal axis), the shape of the lens will cause the light to bend so that it passes through a point known as the focal point.  For every lens there is only one focal point, and the distance between the focal point and the lens is known as the focal length.  This is shown in Figure 2.

Objects reflect rays of light in all directions.  When rays of light reflected off a nearby object hit a convex lens the features of the lens cause the rays of light to converge on the other side of the lens in such a way that the object appears upside down, as in Figure 3.  The image will appear sharp (focused) at a distance that depends on the focal length of the lens and how far away the object is from the lens.  This is essentially how cameras work.  They bend the light so that it appears focused on a film or, in the case of digital cameras, a sensor.

Figure 3

Now that we know the basics of how lenses work, we can look at commercial camera lenses and see what f-stops are.

References

• Focal Length and F-Stop Explanation
• How Cameras Work from HowStuffWorks
• Focal Length from Wikipedia
• Lens (Optics) from Wikipedia

Licenses

• Figure 2 was adapted from
  http://en.wikipedia.org/wiki/File:Focal-length.svg and is licensed under
  the Creative Commons Attribution ShareAlike 3.0 License.
• Figure 3 was taken from
  http://upload.wikimedia.org/wikipedia/en/thumb/7/71/Lens3.svg/550px-Lens3.svg.png and is licensed under
  the Creative Commons Attribution ShareAlike 3.0 License.