The next important particular that must be known with regard to a lens is its effective aperture, or the size of the largest parallel pencil of light that the lens and stop together will pass. Knowing this for each stop we can estimate relative exposures with different stops, for the amount of light passing the lens varies with the area of the pencil, and the exposure must vary inversely with the amount of light. For example, if we so alter the aperture as to double the area of the light pencil twice as much light passes and only half as much exposure is required. As the area of the aperture must vary with the square of its diameter it is sufficient to know the diameter only, and this dimension is best expressed as a fraction of the focal length. This, therefore, is the meaning of the fractions f/8, f/11, f/16, f/22, etc, by which the apertures of lenses are always represented. The f stands stands for focal length and the fraction simply denotes that the effective aperture is 1/8 th, rxth, ^cth, etc. of the focal length. The denominator of the fraction is the "ratio number" of the stop.
An f/8 aperture is naturally twice the diameter of an f/16 aperture; it is, therefore, four times the area, passes four times as much light, and requires one-fourth as much exposure. An f/11 aperture (reallyf/11"3) is half the area of f/8 and twice that of f/16. Therefore, by changing from f/S to f/11, or from f/11 to f/16, we reduce the light by one-half and must double the exposure. These stops belong to a universally useful series in which each stop requires twice the exposure of the next larger one, the series being f/4,f/5-6,f/8, f/11.3,f/16,f/22-6,f/32,f/45.2, //64. The stops in modern lenses belong to this series, with the occasional exception of the largest stop, which, in rapid lenses, being simply the biggest one that can be used, will not always fit in.
The effective aperture is the size of the hole in the stop plate only when the stop is in front of the lens. To measure the true effective aperture in other cases first focus on a very distant object, then replace the focussing screen by some sort of thin opaque screen perforated in the centre with a small pin-hole. Put a bright light behind the pinhole, then lay a piece of ground glass flat against the hoed of the lens, and measure the diameter of the circular disc of light seen on this little screen; this will be the diameter of the effective aperture.
The effective aperture for a distant object forms the basis of calculations in the case of near objects, but the result is sometimes wrong owing to the fact that, with certain lenses, the effective aperture really varies with the distance of the object. To test whether the aperture is thus " inconstant " or not, measure it just as described above, first with the lens in its usual position, and then again with the lens reversed so that the hood points to the pin-hole. If the two measurements agree the aperture is constant for any distance of the object, but if the first measurement is larger than the second then the aperture is smaller for near objects, while if the second measurement is the greater the aperture increases with near objects. Excepting with a few lenses of very special type, inconstancy is only a matter of moment when copying or enlarging, for which work an inconstant lens is not at all desirable. With certain lenses, however, inconstancy is so great that it must be allowed for; the " Telephoto " lens being a notable example.
When the aperture alone is varied exposure varies with the square of the ratio number of the stop. Thus the relative exposures withf/8 andf/16 are as 64 : 256, or as 1 : 4.
If with the same stop we alter the focal distance from lens to plate by focussing on a different distance, exposure varies with the square of the focal distance of the plate. Thus, if we rack out the camera from 7 in. to 10 in. exposure must be increased in the ratio of 49 : 100, or must be approximately doubled.
When copying to various scales with any one stop exposure varies with the square of 1 plus the ratio of image to object. Thus if at one time the image is half full size and at another three times full size, exposures vary in the ratio of (1 +%)2 to (1 + 3)2, or in that of 2 1/4 to 16.
So long as the aperture has the same ratio to the focal distance of the plate exposure is constant, whether the same lens is used or not. Therefore with two different lenses both with f/8 apertures and both focussed on distant objects exposure is equal, but if one lens is focussed on a near distance the camera is racked out and the focal distance increased, and then a longer exposure is required.
Relative exposure with pin-holes may be calculated in the same way as with lenses, the distance of plate from pinhole divided by the diameter of the latter being the " ratio number".
To a certain extent the rapidity of lenses varies, apart from inconstancy, with the materials used.and sundry small structural details, but the variation is generally so small that it can be neglected. Nevertheless, when a very large aperture is in use and an exceedingly brief exposure is given the result may be affected to an appreciable extent by these small variations, and this is a matter of some moment to those who have to deal with high-speed work. Some lenses at//6*5 seem to be quite as rapid as others at f/6, but the differences are more marked when apertures of between //4 and // 5 are in question.