Page 406 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 31] SPHERICAL MIRRORS 391

In general, an object placed between the focal point and the center of curvature C of a concave mirror (that is,
with p greater than f but less than 2 f ) will have a real, inverted image that is larger than the object.

Fig. 31-7

SOLVED PROBLEM 31.5

A pencil 12 cm long is placed at the center of curvature of a concave mirror whose focal length is 40 cm.
Find the location, size, and nature of the image.

Since f = R/2 for a concave mirror, p = R = 2 f = 80 cm here. The image distance is therefore
pf (80 cm)(40 cm)
q = = = 80 cm
p − f 80 cm − 40 cm
The image is real and at the same distance from the mirror as the object (Fig. 31-8). The height of the image is
q 80 cm
h =−h =−(12 cm) =−12 cm

p 80 cm
which is the same as the height of the object. The minus sign indicates an inverted image.
In general, an object placed at the center of curvature of a concave mirror has a real, inverted image the same
size as the object and at the same distance from the mirror.

Fig. 31-8 Fig. 31-9

SOLVED PROBLEM 31.6
A cigar 15 cm long is placed 75 cm in front of a concave mirror whose focal length is 30 cm. Find the
location, size, and nature of the image.
Here p = 75 cm and f = 30 cm, so the image distance is
pf (75 cm)(30 cm)
q = = = 50 cm
p − f 75 cm − 30 cm
The image is real and on the same side of the mirror as the cigar (Fig. 31-9). The length of the image is
q 50 cm

h =−h =−(15 cm) =−10 cm
p 75 cm
which is smaller than the length of the cigar. The minus sign indicates an inverted image.

SOLVED PROBLEM 31.7
A reflecting telescope that uses a concave mirror whose radius of curvature is 4 m produces an image
of the moon on a photographic plate. The moon’s diameter is approximately 3500 km, and it is about