Understanding F-Numbers: Aperture, Light Exposure, and Depth of Field

When a lens is described with a number like f/5.6 or f/1.8, it refers to the f-stop or aperture setting of the lens. The f-stop number indicates the size of the lens' aperture, which is the opening that allows light to enter the camera.

Key Points:

Aperture Size: The f-stop number is the ratio of the lens' focal length to the diameter of the aperture. A lower f-stop number, such as f/1.8, means a larger aperture, allowing more light to enter, while a higher f-stop number, such as f/5.6, indicates a smaller aperture, allowing less light. Light Exposure: A larger aperture, with a smaller f-stop number, results in better performance in low light conditions and allows for faster shutter speeds. Conversely, a smaller aperture with a larger f-stop number reduces the amount of light, which may require slower shutter speeds or higher ISO settings. Depth of Field: The f-stop also affects depth of field, which is the range of distance within a photo that appears sharp. A lower f-stop, larger aperture, creates a shallower depth of field resulting in a blurred background bokeh effect. A higher f-stop, smaller aperture, increases depth of field, keeping more of the image in focus.

F-Number in Lens Speed

If a lens is said to be f/1.8, that is the lens speed, i.e., the maximum aperture the lens has. Zoom lenses often have the speed marked with two values like f/3.5–5.6. This means the speed at the widest is f/3.5 and at the long end is f/5.6. The speed gradually reduces when you zoom in.

Historical Context and Technical Details

There are two chief numbers for describing a lens: the first is the focal length, universally given in millimeters these days. The second is the proportion of the focal length to the maximum diameter of the lens, written as a ratio, such as 1:1.8 or as a fraction, f/1.8. The f here stands for "focal length," and the slash shows that it's a fraction. Why is it a ratio or fraction rather than a measurement of the actual diameter as with binoculars or telescopes? It's because what matters for determining the exposure time for making a photograph is how bright the image is. The ratio of lens diameter to focal length is what determines the brightness. Therefore, all lenses with a ratio of lens opening to focal length of 1:1.8 will make an image of the same brightness, requiring the same exposure time for a sensor of the same light sensitivity.

A lens of short focal length makes a small image. Although an f/1.8 lens of short focal length has a physically small opening, the light that comes through it is spread out less than with a longer focal length lens with a correspondingly bigger opening.

Note that the f/number is a ratio of diameter to focal length, but the amount of light that gets in varies with the area of the opening. So it follows a square rule, with each step representing an effective doubling of the light-admitting area. This is why the familiar run of f/stops goes in steps of 1.4, approximately the square root of 2.

Most lenses are fitted with a device to reduce the area of the opening, called a diaphragm. This is calibrated in f/ratios. So if a lens is said to be f/1.8, it means that the biggest opening we can get is equal to the focal length of the lens divided by 1.8.

The maximum opening of the lens is often not one of the numbers on the regular sequence (1, 1.4, 2, 2.8, 4) because manufacturers typically make the maximum opening as wide as possible given cost, size, and image quality constraints. There's nothing magical about the current f/number series, and historically, different series were used.

Additional Insights

The physical size of the lens opening is more important for certain aspects of photography, but for exposure, the f/number is what counts. For example, in focal length, think of a simple lens like a magnifying glass or the lens on a box camera. If you hold one of these lenses in front of a sheet of paper and make an image of a distant object, you need to move the lens towards or away from the paper to get the image sharp. The distance between the lens and the image plane when the image of a distant object is sharp is called the focal length.

The longer the focal length, the bigger the image. This is important for photographic purposes like counting tanks in pictures from a satellite or wildlife photography, where you either can't get close to your subject (birds, numbats) or don't want to (lions, crocodiles). In much photography, a longer lens will have a narrower field of view, and a lens with a shorter focal length will have a wider field of view, assuming it's designed properly for that sensor size.

Now it gets really complicated. In the old days of film, there were only a few image sizes that mattered, and amateur/enthusiast photography was often done on 35mm film with an image size of 24mm x 36mm called Full Frame. When digital came in, cameras were made with a much larger range of image sizes, and the way most of these sizes is specified is based on an obsolete TV technology. A lens on a tiny camera with a focal length of 5mm might have the same field of view as a lens on a big camera of 28mm. Instead of specifying the field of view, the manufacturers and people who write about equipment often describe the field of view as that of an equivalent lens on a Full Frame camera.

For calculating f-stops, the real focal length counts, not any equivalent. Understanding these concepts is crucial for photographers looking to control exposure and artistic effects in their images.