Archived posting to the Leica Users Group, 2001/07/16
[Author Prev] [Author Next] [Thread Prev] [Thread Next] [Author Index] [Topic Index] [Home] [Search]> -----Original Message----- > From: Ethel Red [mailto:ethel_red@hotmail.com] > f:1 means that the diameter of the aperture is the same as > the focal length. > It's a fraction actually. f:2 means the diameter of the > aperture is 1/2 the > focal length. At 1/2 the diameter, the area is 1/4 thereby > letting in 1/4 as > much light, or two full stops. > > PJW > > > > _________________________________________________________________ This explains the commonly used notation f/x, where x is the stop number. Focal length multiplied by the relative diameter of the aperture ( f * 1/x = f/x ). Since the area of a circle is represented by the equation A = pi * r^2 = pi * (d/2)^2 = pi * d^2 / 4 Abandoning units for the momement, a diameter of 1 results in A1 = pi * 1^2 / 4 = pi/4 While a diameter of 1 / sqrt(2) yields... A2 = pi * (1/sqrt(2))^2 /4 = pi * 1/2 / 4 = pi/8 And clearly... A1 = 2 * A2 So the area difference between relative diameters of 1 and 1/sqrt(2) is a factor of 2. An aperture of A1, which corresponds to f/1, lets through twice as much light as A2, with an apeture corresponding to f/sqrt(2) ~= f/1.4.