Aconverging lens of focal length 20 cm is placed in contact with, and to the left of, a diverging lens of focal length 30 cm. if an object is placed 40 cm to the left of the converging lens, the total magnification is:
a) –3.0
b) –1.5
c) –1.0
d) 2.0
e) 3.0

The total magnification = -3.0

Explanation:

Since the lenses are in contact, the combined focal length, f, of the two lenses is given by,

1/f = 1/f₁ + 1/f₂, where f₁ and f₂ are the focal lengths of the two lenses.

1/f = 1/20 + 1/-30

1/f  = (-3 + 2)/-60 = -1/-60

1/f  = 1/60

f = 60cm

magnification = image distance/object distance = v/u

where u = 40cm, v = ?

Using the mirror, 1/f = 1/v + 1/u

1/60 = 1/v + 1/40

1/v = 1/60 - 1/40

1/v = ( 2 - 3)/120 = -1/120

v = -120cm

Therefore, magnification = -120cm/40cm

magnification = -3.0

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