How f-numbers work?

Understanding F-Numbers in Photography

The f-numbers in photography represent the ratio of the lens’s focal length to the diameter of the effective aperture. For instance, f/2 signifies that the aperture’s diameter is half the focal length, while f/4 indicates a quarter. This system integrates two crucial elements that determine image brightness:

1. Distance from the Objective to the Image: For distant subjects (focused at infinity), the image is formed at the focal length from the lens. According to the inverse square law of light, doubling the distance between a surface and a light source reduces the light it receives to a quarter. Therefore, a lens with a 100mm focal length produces an image that is a quarter as bright as that formed by a 50mm lens.
2. Diameter of the Bright Beam: Doubling the diameter of an aperture increases its area by a factor of four. Thus, lenses with relative apertures of f/8 (e.g., 100/12 and 50/6) produce images of equivalent brightness. The f-number is derived from the formula:
   f-number = focal length / effective aperture diameter 

In practice, the correlation between f-number and brightness deteriorates when photographing subjects up close because the lens-to-image distance significantly deviates from the focal length.

Historically, f-number settings were referred to as “stops”. Before the invention of iris diaphragms, stops were thin pieces of perforated metal inserted into a slot in the lens barrel to achieve the desired aperture size. Thus, photographers use the term “stopping down” to refer to reducing the aperture size and “opening up” to increasing it.

Modern camera lenses typically stop at f/16 or f/22, while larger lenses can go down to f/32 or f/45. Smaller apertures increase the depth of field but can cause diffraction, which degrades image detail. Consequently, no lens is designed to stop down to the size of a pinhole.

The maximum aperture f-number, along with the focal length, name, and part number, is engraved on the edge of the lens. Within the same brand and focal length, two lenses can vary significantly in cost if one has a maximum aperture that is one stop wider. This difference in price reflects the higher capability to capture photos in low light or use faster shutter speeds. Additionally, “faster” lenses often boast superior overall optical quality.

For digital SLRs, high-quality optics are particularly beneficial, balancing performance against price.