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The Barnet Book of Photography A Collection of Practical Articles

Should be divided into the focal length


focal length of all lenses (except to a very small extent, with single or so-called "landscape" lenses) is proportional to the linear dimension of the image that it gives under similar conditions. For example, a lens of 6 inches focal length will give just the same amount of subject on a quarter plate that a lens of 12 inches focal length will give on a whole plate, because the linear measurement of the whole plate is exactly double that of the quarter plate. The easiest way to compare the focal lengths of two lenses, is to focus both on a fairly distant object or view, and to measure in the image the distance between two fixed points in both cases. The proportion between these measurements is the proportion between the focal lengths of the lenses. By this method the focal length of any lens can easily be determined if one has a lens of known focal length.

If a lens is first focussed on a distant object, and the focussing screen is then moved back until the image of any object is of the same size as the object, the distance travelled by the focussing screen is exactly the focal length of the lens. It is however exceedingly difficult to get at the same time an image of an exactly predetermined size, and to secure the very best definition, so that it is more convenient to get the image as near as it happens to come to the size of the object and then to allow for the difference, as then nothing interferes with the operation of focussing. The best

near object to use is an accurately divided scale, and the details wanted in addition to those mentioned above are the comparative lengths of the image and the object. To get these, two fine marks are made on the focussing screen, and the distance between these is the length of the image. The scale is focussed with critical exactness and so that it falls over these marks, then the amount of the scale represented between the marks can be measured, and the divisions counted for the length of the object. The distance over which the focussing screen was moved between the two focussings is to be multiplied by the length of the object and divided by the length of the image, and the result is the focal length of the lens.

_Aperture._--The "aperture" of a lens is the diameter of the cylinder of light that it can receive and transmit. If the diaphragm is in front of the lens, the hole in the diaphragm is the aperture, but if the diaphragm is behind a part of the lens, so that the incident light passes through a lens first, the hole in the diaphragm is not the "aperture," the "aperture" is larger because the lens condenses the light before it gets to the diaphragm. The aperture of any lens can be measured by focussing a distant object, then replacing the focussing screen by a sheet of cardboard with a pinhole in the middle of it. In a dark-room a light must be placed behind the pinhole, and a bit of ground glass held in front of the lens. A disc of light will be seen on the ground glass and the diameter of this is the diameter of the aperture, or simply, the "aperture," with the diaphragm employed.

_Rapidity._--The rapidity of a lens depends almost wholly on its focal length and aperture. The thickness of the glass makes a little difference, and at every surface in contact with air there is loss by reflection, but these and analogous matters are of comparatively little importance, and as they are uncertain and cannot be determined it is customary to refer rapidity to the focal length and aperture only. The aperture found, that is, the diameter of the effective incident cylinder of parallel rays, should be divided into the focal length, and the diaphragm corresponding to the aperture should then be marked with a fractional expression indicating the proportion of aperture to focal length. Thus if the aperture is one eighth the focal length, it is marked _f_/8, if a sixteenth _f_/16, and so on. All lenses with the same aperture as so marked may be regarded as of equal rapidity whatever their focal lengths may be. Now the more rapid a lens is the shorter the exposure that it is necessary to give for any subject, and the exposure required is proportional to the square of the figure in the expressions as given above. Namely 8 and 16 squared give 64 and 256 which are as one to four, the proportional exposures required. Or we may say that 8 to 16 are as 1 to 2 and square these and get 1 to 4 the proportional exposures.

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