We are now in a position to understand how virtual images are formed, and the formation of a virtual image by means of a convex lens will be readily followed from a { 137} study of Fig. 73. Let L represent a double convex lens, with an object, AB, placed between it and the point F, which is the principal focus of the lens. The rays from the object AB are refracted on passing through the lens, and again refracted on leaving the lens, so that an image of the object is formed at the eye, N. As it is impossible for the eye to follow the bent rays from the object, a virtual image is formed and is seen at A^1B^1, and is really a continuation of the emergent rays. The magnifying power of such a lens may be found by dividing 6 inches by the focal length of the lens, 6 inches being the distance at which we see small objects most distinctly. A lens having a focal length of 1/4 inch would magnify 24 times, and one with a focal length of 1/100th of an inch 600 times, and so on. The magnifying power is greater as the lens is more convex and the object near to the principal focus. When a single lens is applied in this manner it is termed a _single microscope_, but when more than one lens is employed in order to increase the magnifying power, as in the telescope, then the apparatus is termed a _compound microscope_.
Unlike a convex lens, which can form both real and virtual images, a concave lens can only produce a virtual image; and while the convex lens forms an image larger { 138} 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 A^1B^1. 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 { 139} are used for photographic purposes the aberration has to be very carefully corrected.