FOCAL LENGTH (Pr., f.ongueur du foyer ; Ger., Brennweite) The distance between the centre of a lens and the screen or plate upon which the image of a distant object is sharply depicted. This defini tion, however, is only correct in the case of a very thin lens, in which the thickness of the glass does not come into consideration, and in which there is only one element. In the case of modern photographic lenses, " focal length " is often taken to mean " equivalent " focal length ; that is to say, when a lens will render the image of a distant object on exactly the same scale as would a very thin spectacle lens, the two are said to be of the same equivalent focal length. Equivalent focal lengths vary in direct proportion to the size of the image obtained; thus, assuming that a 6-in. lens gives a 3-in. image of a distant object, an x8-in. lens will give a 9-in. image of the same object. This fact enables the measurement of the focal length of any lens to be effected by simple com parison of its image with a similar image made by a lens of known focal length, or, better still, with a pinhole image. A practical method is to substitute for the lens a fairly small pinhole, the camera being extended to a convenient length (a length of Jo in. simplifies the slight calculation necessary), and to take a negative of some distant object having two easily recognisable points, such as chimneys or telegraph poles, these being shown a few inches apart. The distance between these two points is carefully measured and becomes a constant factor in determining the focal length of any other lens which can be focused upon the same object. Assume that the
distance between the points is 4.5 in. Taking a lens of unknown focal length, it may be found, for example, that the images of the two selected points are 3 in. apart ; then as 4.3 is to 3 so is xo to x. 3 x io -4- = 6.66 in. An approxi mately correct result may be obtained by focus ing a near object so that it appears in natural size upon the screen ; then one-fourth of the distance between the object and the focusing screen is the focal length of the lens.
The focal length of negative lenses may be ascertained by neutralising them by placing positive lenses in contact with them until one is found that practically loses its convergent powers ; then the concave lens is said to have a negative focal length equal to that of the positive lens which it neutralises. Dallmeyer's method is to place a diaphragm, containing two small openings, in contact with the negative lens, which is then turned to the sun ; the light pass ing through these two small openings is received upon a white card, which is moved away from the lens until the two spots of light are double the distance apart as compared with the open ings in the diaphragm ; then the distance between the diaphragm and the card is the negative focal length