Question

A converging 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

Answer 1

Answer: The total magnification = -3.0

Step-by-step 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