Page 415 - Schaum's Outline of Theory and Problems of Applied Physics

400 LENSES [CHAP. 32

Table 32-1

Quantity Positive Negative

Focal length f Concave lens Diverging lens
Object distance p Real object Virtual object
Image distance q Real image Virtual image
Magnification m Erect image Inverted image
Height h Erect image Inverted image

SOLVED PROBLEM 32.8
A coin 3 cm in diameter is placed 24 cm from a converging lens whose focal length is 16 cm. Find the
location, size, and nature of the image.

Here p = 24 cm and f =+16 cm, so the image distance is
pf (24 cm)(16 cm)
q = = = 48 cm
p − f 24 cm − 16 cm

The image is real since q is positive (Fig. 32-6). Since m = h /h =−q/p, the diameter of the coin’s image is
q 48 cm

h =−h =−(3cm) =−6cm
p 24 cm

The image is inverted (since h is negative) and twice as large as the object.
In general, an object that is a distance between f and 2 f from a converging lens has a real, inverted image that
is larger than the object.

F′ 2F′
2F F

Fig. 32-6

SOLVED PROBLEM 32.9
A sardine 8 cm long is 30 cm from a converging lens whose focal length is 15 cm. Find the location, size,
and nature of the image.

Here p = 30 cm and f =+15 cm, so the image distance is
pf (30 cm)(15 cm)
q = = = 30 cm
p − f 30 cm − 15 cm
The image is real since q is positive (Fig. 32-7). The length of the sardine’s image is
q 30 cm
h =−h =−(8cm) =−8cm

p 30 cm

The image is inverted (since h is negative) and is the same size as the object.

F′ 2F′ F′ 2F′
2F F 2F F

Fig. 32-7 Fig. 32-8