be inverted, since it is impossible for the rays from the end,
M, of the object to be carried by refraction to the upper end of the image
at _n_. The relative positions of the object and image when placed at
different distances from the lens are exactly the same as the conjugate
foci of light rays as shown in Fig. 69.

[Illustration: FIG. 71.]

The length of the image formed by a convex lens is to the length of the
object as the distance of the image is to the distance of the object from
the lens. For example, if a lens having a focal length of 12 inches is
placed at a distance of 1000 feet from some object, then the size of the
image will be to that of the object as 12 inches to 1000 feet, or 1000
times smaller than the object; and if the length of the object is 500
inches, then the length of the image will be the 1/1000th part of 500
inches, or 1/2 inch. {134}

The image formed by the convex lens in Fig. 71 is known as a _real image_,
but in addition convex lenses possess the property of forming what are
termed _virtual images_. The distinction can be expressed by saying, _real
images are those formed by the refracted rays themselves, and virtual
images those formed by their prolongations_. While a real image formed by a
convex lens is always inverted and smaller than the object, the virtual
image is always erect and larger than the object. The power possessed by
convex lenses of forming virtual images is made use of in that useful but
common piece of apparatus known as a reading or magnifying glass, by which
objects placed within its focus are made larger or magnified when viewed
through it; but in order to properly understand how objects seem to be
brought nearer and apparently increased in size, we must first of all
understand what is meant by the expression, _the apparent magnitude of
objects_.

[Illustration: FIG. 72.]

The apparent magnitude of an object depends upon the angle which it
subtends to the eye of the observer. The image at A, Fig. 72, presents a
smaller angle to the eye than the angle presented by the object when moved
to B, and the image therefore appears smaller. When the object is moved to
either B or C, it is viewed under a much {135} greater angle, causing the
image to appear much larger. If we take a watch or other small circular
object and place it at A, which we will suppose is a distance of 50 yards,
we shall find that it will be only visible as a circular object, and its
apparent magni