3. An object of 6 cm height is placed 50 cm away from a diverging concave lens of focal length of 25 cm. Find the position, nature and height of the image produced.
Solution
Position: 1
__ u − 1
____ 50 − 1
1
____ 50 + 1
1 1
____ 50 = 1
3
____ 50 + 2
__ v
3v = 50 v = 16 2
__ u
__ 3 cm from lens (virtual)
Magnification: m = v
m =
_____ 50
16 2 m = 1
_ 3
∴ Height of image = 1
__ 3 times magnification
__ 3 × 6 cm = 2 cm
You may now complete Exercise 15B (page 164). Uses of concave lenses
As with convex lenses, concave lenses can be used in a variety of optical instruments but are mainly used in spectacles. They are also used in telescopes and camera lenses (Fig. 15.14), and in door peepholes (Fig. 15.15).
__ v = − 1
__ f
__ v = − 1
____ 25 = 1
____ 50 = 1
__ v
__ v
____ 25
H
4. An image half the size of the object is formed in a concave lens of focal length 25 cm. Calculate the object and image distance.
Solution First use m = v other: 1
__ 2 = v
__ u − 1
____ 2v − 1
1
__ v = − 1
__ f .
__ u to write u or v in terms of the
__ u ⇒ u = 2v
Now substitute 2v for u in the optics formula 1
__ v = − 1
____ 25 ⇒ 1
____ 2v − 2
____ 2v = − 1
____ 25 ⇒ − 1
This gives −25 = −2v, so v = 12.5 cm. Since u = 2v, u = 25 cm.
____ 2v = − 1
____ 25
FIG. 15.14 Cameras use concave lenses 160 FUSION
FIG. 15.15 Concave lenses are used in door peepholes
