[Illustration: FIG. 110.--Showing how the position of the image alters
relatively to the position of the object.]

From what has been said above we deduce two main conclusions--(1.) The
nearer an object is brought to the lens, the further away from the lens
will the image be. (2.) If the object approaches within the principal
focal distance of the lens, no image will be cast by the lens. To make
this plainer we append a diagram (Fig. 110), which shows five positions
of an object and the relative positions of the image (in dotted lines).
First, we note that the line A B, or A B^1, denotes the principal
focal length of the lens, and A C, or A C^1, denotes twice the focal
length. We will take the positions in order:--

_Position I._ Object further away than 2_f_. Inverted image _smaller_
than object, at distance somewhat exceeding _f_.

_Position II._ Object at distance = 2_f_. Inverted image at distance =
2_f_, and of size equal to that of object.

_Position III_ Object nearer than 2_f_. Inverted image further away than
2_f_; _larger_ than the object.

_Position IV._ Object at distance = _f_. As rays are parallel after
passing the lens _no_ image is cast.

_Position V._ Object at distance less than _f_. No real image--that is,
one that can be caught on a focussing screen--is now given by the lens,
but a magnified, erect, _virtual_ image exists on the same side of the
lens as the object.

We shall refer to _virtual_ images at greater length presently. It is
hoped that any reader who practises photography will now understand why
it is necessary to rack his camera out beyond the ordinary focal
distance when taking objects at close quarters. From Fig. 110 he may
gather one practically useful hint--namely, that to copy a diagram,
etc., full size, both it and the plate must be exactly 2_f_ from the
optical centre of the lens. And it follows from this that the further he
can rack his camera out beyond 2_f_ the greater will be the possible
enlargement of the original.

CORRECTION OF LENSES FOR COLOUR.

We have referred to the separation of the spectrum colours of white
light by a prism. Now, a lens is one form of prism, and therefore sorts
out the colours. In Fig. 111 we assume that two parallel red rays and
two parallel violet rays from a distant object pass through a lens. A
lens has most bending effect on violet rays and least on red, and the
other colours of the spectrum are intermediately influenced. For the
sa