Use the law of reflection to prove that the focal length of a mirror is half its radius of curvature. That is, prove that f= R/2. Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature.

Transcribed Image Text:

The Law of Reflection The angle of reflection equals the angle of incidence. When we see ourselves in a mirror, it appears that our image is actually behind the mirror. This is illustrated in Figure 25.9. We see the light coming from a direction determined by the law of reflection. The angles are such that our image is exactly the same distance behind the mirror as we stand away from the mirror. If the mirror is on the wall of a room, the images in it are all behind the mirror, which can make the room seem bigger. Although these mirror images make objects appear to be where they cannot be (like behind a solid wall), the images are not figments of our imagination. Mirror images can be photographed and videotaped by instruments and look just as they do with our eyes (optical instruments themselves). The precise manner in which images are formed by mirrors and lenses will be treated in later sections of this chapter. FIGURE 25.9 Mirror Image