Page 403 - Schaum's Outline of Theory and Problems of Applied Physics

388 SPHERICAL MIRRORS [CHAP. 31

OBJECTS AND IMAGES
A spherical mirror can produce an image of an object placed in front of it. A real object is located in front of a
mirror. A virtual object seems to be located behind the mirror and must itself be an image produced by another
mirror or lens. A real image is formed by light rays that actually pass through the image, so a real image will
appear on a screen placed at the position of the image. A virtual image can be seen only by the eye since the
light rays that seem to come from the image do not actually pass through it. Real images are located in front of
a mirror; virtual images seem to be located behind it.

RAY TRACING
The position and size of the image formed by a spherical mirror of an object in front of it can be found by
constructing a scale drawing. What is done is to trace two different light rays from each point of interest in the
object to where they (or their extensions, in the case of a virtual image) intersect after being reflected by the
mirror. Three rays especially useful for this purpose are shown in Fig. 31-3; any two are sufficient:
1. A ray that leaves the object parallel to the axis of the mirror. After reflection, this ray passes through the
focal point of a concave mirror or seems to come from the focal point of a convex mirror.
2. A ray that passes through the focal point of a concave mirror or is directed toward the focal point of a
convex mirror. After reflection, this ray travels parallel to the axis of the mirror.
3. A ray that leaves the object along a radius of the mirror. After reflection, this ray returns along the same
radius.

Fig. 31-3

SOLVED PROBLEM 31.1
What is spherical aberration?

Spherical aberration refers to the fact that light rays from a point on an object that are reflected at different
distances from the axis of a spherical mirror do not converge to (or appear to diverge from) a single point. This effect
is shown in Fig. 31-4(a) for parallel rays reaching a concave mirror: Rays reflected from the outer parts of the mirror
converge at focal points closer to the mirror than those reflected near the mirror’s axis. As a result, a spherical mirror,
which has a circular cross section, produces sharp images only close to the mirror axis. Concave mirrors whose cross
sections are parabolic as in Fig. 31-4(b), do not suffer from spherical aberration and are used when high-quality
images are required, for instance, in telescopes.