3. f-number and numerical aperture of a lens.The size of a lens determines its light-gathering power and, consequently, the brightness of the image it forms. Two commonly used indicators of this special characteristic of a lens are called the f-number and the numerical aperture.

The f-number, also referred to as the relative aperture and the f/stop, is defined simply as the ratio of the focal length f of the lens, to its diameter D, as given in Equation 3-8.

For example, a lens of focal length 4 cm stopped down to an aperture of 0.5 cm has an f-number of 4/0.5 = 8. Photographers usually refer to this situation as a lens with an f stop of f/8. Before the advent of fully automated cameras (“point and shoot”), a photographers would routinely select an aperture size for a given camera lens (thereby setting the f stop), a shutter speed, and a proper focus to achieve both the desired image brightness and sharpness.

Table 3-2 lists the usual choices of f stops (f-numbers) available on cameras and the corresponding image irradiance or “brightness” in watts per square meter. The listing gives the irradiance E0 as the value for an f stop of 1 and shows how the image irradiance decreases as the lens is “stopped down,” that is, as the adjustable aperture size behind the camera lens is made smaller. From Equation 3-8, it should be clear that, for a given camera lens of focal length f, the f stop or f-number increases as D decreases, that is, as the aperture size decreases. Clearly then, increasing the f-number of a lens decreases its light-gathering power.

Since the total exposure in joules m2 on the film is the product of the irradiance in joules (m2-s) and the exposure time (shutter speed) in seconds, a desirable film exposure can be obtained in a variety of ways. Accordingly, if a particular film whose speed is described by an ASA number is perfectly exposed by light from a particular scene with a shutter speed of 1/50 second and an f stop of f8 (irradiance equals E064 from Table 3-2), it will also be perfectly exposed by any other combination that gives the same total exposure. For example, by choosing