Page 26 - Modern Optical Engineering The Design of Optical Systems

Optics Overview 9

Figure 1.8 The passage of a wave front through a converging, or posi-
tive, lens element.

located. In each interval of time the wave front may be assumed to
travel a distance d 1 in the medium of the source; it will travel a lesser
distance d 2 in the medium of the lens. (As in the preceding discussion,
these distances are related by n 1 d 1 n 2 d 2 .) At some instant, the vertex
of the wave front will just contact the vertex of the lens surface at
point A. In the succeeding interval, the portion of the wave front inside
the lens will move a distance d 2 , while the portion of the same wave
front still outside the lens will have moved d 1 . As the wave front passes
through the lens, this effect is repeated in reverse at the second surface.
It can be seen that the wave front has been retarded by the medium of
the lens and that this retardation has been greater in the thicker central
portion of the lens, causing the curvature of the wave front to be
reversed. At the left of the lens the light from P was diverging, and to
the right of the lens the light is now converging in the general direc-
tion of point P′. If a screen or sheet of paper were placed at P′, a concen-
tration of light could be observed at this point. The lens is said to have
formed an image of P at P′. A lens of this type is called a converging,
or positive, lens. The object and image are said to be conjugates.
Figure 1.8 diagrams the action of a convex lens—that is, a lens
which is thicker at its center than at its edges. A convex lens with an
index higher than that of the surrounding medium is a converging
lens, in that it will increase the convergence (or reduce the divergence)
of a wave front passing through it.
In Fig. 1.9 the action of a concave lens is sketched. In this case the
lens is thicker at the edge and thus retards the wave front more at the
edge than at the center and increases the divergence. After passing
through the lens, the wave front appears to have originated from the
neighborhood of point P′, which is the image of point P formed by the
lens. In this case, however, it would be futile to place a screen at P′ and