Page 148 - Modern Optical Engineering The Design of Optical Systems

Prism and Mirror Systems 131

Figure 7.8 The reflected image
is inverted top to bottom, but not
left to right.

The preceding discussion has treated reflection from the standpoint
of an observer viewing a reflected image. Since the path of light rays
is completely reversible, we can equally well consider point P′ in Fig. 7.6
to be an image formed by a lens at the right. Then P would be the
reflected image of P′. Similarly in Figs. 7.7 and 7.8, we may replace
the eye with a lens the image of which is the primed figure (A′B′ or
A′B′C′D′) and view the unprimed figures as their reflected images.
A point worth noting is that reflection constitutes a sort of “folding”
of the ray paths. In Fig. 7.9, the lens images the arrow at AB. If we now
insert reflecting surface MM′, the reflected image is at A′B′. Notice that
if the page were folded along MM′, the arrow AB and the solid line rays
would exactly coincide with the arrow A′B′ and the reflected (dashed)
rays. It is frequently convenient to “unfold” a complex reflecting system;
one advantage of this device is that an accurate drawing of the ray
paths becomes a simple matter of straight lines.
A useful technique to determine the image orientation after passage
through a system of reflectors is to imagine that the image is a transverse
arrow, or pencil, which is bounced off the reflecting surface, much as a
thrown stick would be bounced off a wall. Figure 7.10 illustrates the tech-
nique. The first illustration shows the pencil approaching and striking the
reflecting surface, the second shows the point bouncing off the reflector

Figure 7.9 The reflecting surface
MM′ folds the optical system.
Note that if the page is folded
along MM′, the rays and images
coincide.