than the object, the concave lens forms an image smaller than the object. Let L, Fig. 74, represent a double concave lens, and AB the object. The rays from AB on passing through the lens are refracted, and they diverge in the direction RRRR, as if they proceeded from the point F, which is the principal focus of the lens, and the prolongations of these divergent rays produce a virtual image, erect and smaller than the object, at A1B1. The principal focal distance of concave lenses is found by exactly the same rule as that given for convex lenses.
Up to the present we have assumed that all the rays of light passed through a convex lens were brought to a focus at a point common to all the rays, but this is really only the case with a lens whose aperture does not exceed 12°. By aperture is meant the angle obtained by joining the edges of a lens with the principal focus. With lenses having a larger aperture the amount of refraction is greater at the edges than at the centre, and consequently the rays that pass through the edges of the lens are brought to a focus nearer the lens than the rays that pass through the centre. Since this defect arises from the spherical form of the lens it is termed spherical aberration, and in lenses that
are used for photographic purposes the aberration has to be very carefully corrected.
The distortion of an image formed by a convex lens is shown by the diagram, Fig. 75. If we receive the image upon a sheet of white cardboard placed at A, we shall find that while the outside edges will be clear and distinct, the inside will be blurred, the reverse being the case when the cardboard is moved to the point B.
Aberration is to a great extent minimised by giving to the lens a meniscus instead of a biconvex form, but as it is desirable to reduce the aberration to below once the
thickness of the lens, and as this cannot be done by a single lens, we must have recourse to two lenses put together. The thickness of a lens is the difference between its thickness at the middle and at the circumference. In a double convex lens with equal convexities the aberration is 167/100ths of its thickness. In a plano-convex lens with the plane side turned towards parallel rays the aberration is 41/2 times its thickness, but with the convex side turned towards parallel rays the aberration is only 117/100ths of its thickness.