A camera lens usually consists of a combination of two or more lenses to produce

Question

A camera lens usually consists of a combination of two or more lenses to produce a good-quality image. Suppose a camera lens has two lenses - a diverging lens of focal length 11.4 cm and a converging lens of focal length 5.70 cm. The two lenses are held 5.71 cm apart. A flower of length 11.4 cm, to be pictured, is held upright at a distance 52.1 cm in front of the diverging lens; the converging lens is placed behind the diverging lens.

a) How far to the right of the convex lens is the final image?

b) What is the magnification of the final image?

c) And what is the height of the final image?

Explanation / Answer

a)
Given
f1 = -11.4 cm (focal length of divering lense)

u1 = 52.1 m (object distance for first lense)

Apply,

1/u1 + 1/v1 = 1/f1

1/u1 = 1/f1 - 1/u1

1/v1 = 1/(-11.4) - 1/52.1

v1 = -9.35 cm (image distance for first lense)

magnification,m1 = -v1/u1 = -(-9.35)/52.1 = 0.179

object disatnce for second lense, u2 = -9.35 - 5.71 = -15.06 cm

f2 = 5.7 cm (focal length of diverging lense)

Again Apply

1/u2 + 1/v2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/5.7 - 1/(-15.06)

v2 = 4.13 ((image distance for second lense) <<<<<---------Answer

magnification,m2 = -v2/u2 = -4.13/(-15.06) = 0.274

b)
overall magnfication, M = m1*m2 = 0.179*0.274 = 0.049 <<<<<<<<<----------Answer

c) image height = M*object height

= 0.049*11.4

= 0.56 cm <<<<<<<<<----------

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