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F-number characterizes the light-gathering power of the lens (Figure 1). This dimensionless quantity is abbreviated frequently as f /# (for example, f /2). For a collimated incident light beam (object at infinity), the f-number is defined by the following equation (for example, Wyatt CL 1991):

 f-number = f / D  (1)

where f is the focal length of the lens (the right focal length in Figure 1). The f-number = 0, corresponds to the maximum gathering power of a lens (at D = ∞ or f = 0).

Numerical aperture geometry
 
Fig. 1. Numerical aperture / f-number geometry. Notation: pp - principal plane of the lens, f - focal plane of the lens. The real part of the refractive index of the medium neighbouring the lens at the right side is m'.

The f-number of a lens is related to the numerical aperture, NA, of the lens as follows (for example, Wyatt CL 1991):

 f-number = 1 / (2 NA)  (2)

The above relationship is valid in the small-angle approximation. [MJ]

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