Question

A combination of two thin lenses with focal lengths f1 and f2 respectively forms an image of
distant obiect at distance 60 cm when lenses are in contact. The position of this image shifts by
10 cm towards the combination when two lenses are separated by 10 cm. The corresponding
values of f1 and f2 are​

Answer 1

The corresponding values of f1 and f2 are 20 cm and - 30 cm respectively.

Explanation:

We are given that:

• Focal lengths f1 and f2 = 60 cm
• Position of image = 10 cm
• Distance between lenses = 10 cm

Solution:

1 / f eq = 1 / f1 + 1 / f2

1 / 60 = 1/ f1 + 1/ f2  ---(1)

Gap of 10 cm

1 / f eq = 1 / f1 + 1/ f2 - d / f1f2

1 / 30 = 1 / 60 - 10 / f1 . f2

10 / f1 . f2 = 1 / 60 - 1/ 30 = 1 - 2 / 60

10 / f1 . f2 = - 1 / 60

f1 . f2 = - 600

60 = f1 . f2 / f1 + f2

f1 + f2 = -600 / 60 = - 10

f1 = 20 cm

f2 = - 30 cm

Thus the corresponding values of f1 and f2 are 20 cm and - 30 cm respectively.