Updated: Dec 6, 2022
The term "f-number" can be confusing, but it's quite simple if you think of it in terms of its three main characteristics: image brightness, image sharpness, and depth of field. F-number is defined as the lens focal length (f) divided by the lens aperture diameter (d). It defines the size of the cone of light that is focused on the image plane and it specifies how much light is let in by the lens in relative terms. So what does all this mean when it comes to optical lenses? Well, with a small f-number, you get a brighter image that is also sharper with a smaller depth of field. With a large f-number, you get a dimmer image that is softer with a larger depth of field.
The f-number is crucial because it allows you to control the exposure of your image. Without this ability, images would be left as either overexposed or underexposed frequently. The f-number also enables you to control the depth of field in your image, which can be very important for getting the right image. The f-number helps to determine the amount of light that enters the lens and therefore has an impact on image brightness and should not be ignored by photographers and engineers. In particular, the f-number affects three specific things. Having a lens with the right f-number is critical in life science or medical applications, where precision and accuracy cannot be compromised.
F-Number and Sharpness
The f-number can influence image sharpness by controlling the way light is focused by the lens. When the diameter of the aperture is larger, the cone angle of the light being focused is also larger. With a larger cone angle of light, the focused spot will be smaller, whereas a small cone of light produces a more prominent focused spot. For example, if you're getting an image of a small item, you'll want to use a smaller f-number so that the image will be sharp. Depending on the scene, you may want to play around with the f-number to get the desired effect, like shallow depth of field or more blurred background. Think of a small f/# corresponding to a sharper image and a larger f/# corresponding to a softer or blurrier image when imagining this concept.
Depth-of-Field and F-Number
The term "depth of field" (DOF) refers to the distance from a lens where the object or subject remains in focus for a fixed focus position of the lens. This is the lens parameter related to the artistic effect called bokeh - when the subject is crisp and sharp, and the background and foreground are softened or blurred. This effect occurs when the f-number is small. Why is that? When the f-number is small, the depth-of-field is also small. This means that objects in front of and behind the focal point will be blurry. With a large f-number, the depth-of-field increases, meaning that objects before and after the focal point will be more in focus. The larger the cone angle, the tighter the focal spot will be; this is how depth of field works with the f-number. Imagine the light coming to a tight focal point and then diverging away from the focal point as it continues to propagate.
The F-Number and Image Brightness
Because the f-number is a ratio of the lens focal length (f) divided by the lens aperture diameter (d), a small f-number means that d is large. This results in more light being let in by the lens and, therefore, a brighter image. A large f-number means that d is small, resulting in less light being let in and a dimmer image. For example, if you're taking a picture in low light conditions, you'll want to use a small f-number so that more light can enter the lens and brighten up the image. With more light, the exposure time needed to form an image is less. Thus a picture can be taken "faster."
A larger aperture results in a smaller f-number. A smaller aperture results in a larger f-number. This might not make intuitive sense at first, but think of it this way: when the diameter (d) is larger, the physical opening in which light enters the lens is also larger. More light equals more photons, which equals a brighter image! So when d is larger, f/# is smaller, and a small f/# leads to a brighter image.
So What the F-Number?
The exposure and depth of field can be controlled by how much light is let into the lens with the aperture. The f-number is simply a ratio between the focal length and the diameter of the lens opening and has a direct impact on image brightness and sharpness.
In summary, a small f-number leads to a brighter image, which is sharper, with a small depth of field. A large f-number results in a dimmer image that is softer and has a large depth of field. So next time you're behind the lens, take some time to consider what f-number you're using and how it will affect your final image. And don't be afraid to experiment - sometimes, the best way to learn is by doing and trying different f-numbers for different effects.