Question

A combination of two thin lenses with focal lengths f₁ and f₂ respectively forms an image of distant object at distance 60 cm when lenses are in contact. The position of this image shifts by 30 cm towards the combination when two lenses are separated by 10 cm. The corresponding value of f₁ and f₂ are–

• A. 30 cm, –60 cm
• B. 20 cm, –30 cm
• C. 15 cm, –20 cm
• D. 12 cm, –15 cm

Answer 1

Answer: (B)

20 cm, –30 cm

Answer 2

$\frac { 1 } { 60 } = \frac { 1 } { \mathrm { f } _ { 1 } } + \frac { 1 } { \mathrm { f } _ { 2 } }$…(i)

and $\frac { 1 } { 30 } = \frac { 1 } { \mathrm { f } _ { 1 } } + \frac { 1 } { \mathrm { f } _ { 2 } } - \frac { 10 } { \mathrm { f } _ { 1 } \mathrm { f } _ { 2 } }$…(ii)

by solving Ist and IInd equation.