Page 402 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 31

Spherical Mirrors

CONCAVE AND CONVEX MIRRORS

The reflecting surface of a concave mirror has the shape of the inside of a sphere. Figure 31-1 shows how a
concave mirror converges a parallel beam of light to a focal point F in front of the mirror. Light passes through
the focal point of a concave mirror, so such a focal point is called real. The distance from the focal point to the
mirror’s surface is the focal length f of the mirror. If the radius of curvature of the mirror is R, its focal length is
given by f = R/2.
The reflecting surface of a convex mirror has the shape of the outside of a sphere. Figure 31-2 shows how
a convex mirror diverges a parallel beam of light so that the reflected rays appear to come from a focal point F
behind the mirror. Because light does not actually pass through the focal point of a convex mirror, such a focal
point is called virtual. The distance from F to the mirror’s surface is the focal length f of the mirror. If the radius
of curvature of the mirror is R, its focal length is given by −R/2; it is considered negative because the focal
point is virtual. Thus

R
Concave mirror : f =+
2
R
Convex mirror : f =−
2
The axis of a mirror of either kind is the straight line that passes through C and F.

R = radius of curvature
C = center of curvature
R = radius of curvature F = virtual focal point
C = center of curvature f = focal length
F = real focal point
f = focal length R
R
F Concave F
mirror
C C

Convex
mirror
f f

Fig. 31-1 Fig. 31-2
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