Most photographers know that F numbers are related to the amount of light reaching the camera’s sensor or film. But a lot of people are still a bit fuzzy about what the number actually represents, and why it’s often such an odd-looking number.  To understand the origin of the F number, you have to go back in time, to the origins of optics, and the humble Magnifying Glass…

The Magnifying glass is a simple convex lens, able to focus on light from a small object, and bend the light so that it can be viewed comfortably from a distance.  Conversely, light from a distant object, like the sun, can be focused by the Magnifying Glass at a short distance from the lens.  This distance is known as the Focal Length (f) of the lens.  Early cameras used small convex lenses in much the same way: light from distant objects was focused onto a light-sensitive plate, and lenses with longer focal lengths produced larger images.

As film emulsions became more sensitive to light, camera makers had to find a way to be able to reduce the light coming into the camera.  So they employed a mechanical iris to block out light coming through the lens.  The amount of light captured by a camera lens is dictated by the area of the iris aperture — to reduce the light entering the camera by half, the iris would reduce the aperture area by half.

Photographers soon discovered that they needed a way of working out the best aperture to use in any given situation, so camera makers needed a system to mark aperture settings, which would be the same for different cameras.

The aperture of a lens (in square inches or millimetres) was not enough to describe how much light produced the image, because longer focal lengths spread the image over a much larger area of the plate, thereby darkening it.  Focal length would have to be taken into account.  Camera makers decided that the best way to show light-gathering power was to describe the F number as the ratio of a lens’s aperture diameter to its focal length.  So, a lens with a 1″ aperture diameter and a 2″ focal length would be marked as f/2 — literally meaning focal length divided by 2.  Stopped down to a ½” diameter, the same lens would be set at f/4, or focal length divided by 4.

This was where the confusion began.  This was not the most easiest-to-understand labelling system for aperture, because the F number apparently increases as the aperture decreases, and its value is not directly proportional to aperture area (because aperture area is proportional to the square of the diameter).  But we’re stuck with it now!

Nowadays, camera lenses have complex designs.  Lenses contain many different lens elements, moving in different directions, effectively changing the apparent focal length and diameter of the lens.  This makes it increasingly difficult to visualise aperture and focal length, with photographers having to rely purely on lens markings and camera displays for aperture settings.

Keith Nuttall, 2009