73.]

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.

[Illustration: FIG. 74.]

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
12deg. 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.

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.

[Illustration: FIG. 75.]

[Illustration: FIG. 76.]

[Illustration: FIG. 77.]

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 {140} 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 1-67/100ths of its thickness. In a pla