34.7.1 Concave Mirrors

FIGURE 34.45 shows a concave mirror, a mirror in which the edges curve toward the light source. Rays parallel to the optical axis reflect from the surface of the mirror so as to pass through a single point on the optical axis. This is the focal point of the mirror. The focal length is the distance from the mirror surface to the focal point. A concave mirror is analogous to a converging lens, but it has only one focal point.

FIGURE 34.45 The focal point and focal length of a concave mirror.

The figure illustrates the focal point and focal length of a concave mirror.
FIGURE 34.45 Full Alternative Text

Let’s begin by considering the case where the object’s distance s from the mirror is greater than the focal length (s>f), as shown in FIGURE 34.46 . We see that the image is real (and inverted) because rays from the object point P converge at the image point P′. Although an infinite number of rays from P all meet at P′, each ray obeying the law of reflection, you can see that three “special rays” are enough to determine the position and size of the image:

FIGURE 34.46 A real image formed by a concave mirror.

The figure illustrates a real image formed by a concave mirror.
FIGURE 34.46 Full Alternative Text

These three rays also locate the image if s<f, but in that case the image is virtual and behind the mirror. Once again, virtual images have a negative image distance s′.

NOTE   A thin lens has negligible thickness and all refraction occurs at the lens plane. Similarly, we will assume that mirrors are thin (even though drawings may show a thickness) and thus all reflection occurs at the mirror plane.