A combination of two thin lenses with focal lengths `f_(1)` and `f_(2)` respectively forms and image of distant object at distance `60cm` 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 values of `f_(1)` and `f_(2)` are

Options

A. `30 cm ,-60cm`
B. `20 cm, -30 cm`
C. `15 cm, -12 cm`
D. `12 cm, -15`

Answer

B

Explanation

Case I:
When lenses in contact,
`(1)/(F)=(1)/(f_1)+(1)/(f_2)`
`(1)/(F)=(1)/(v)-(1)/(u)=(1)/(60)-(1)/(infty)=(1)/(60)`
Case II: When lenses are at separation `d=10cm`,
`(1)/(F')=(1)/(f_1)+(1)/(f_2)-(d)/(f_1f_2)`
`(1)/(F')=(1)/(v)-(1)/(u)=(1)/(30)-(1)/(infty)=(1)/(30)`
`(1)/(f_1)+(1)/(f_2)-(d)/(f_1f_2)=(1)/(30)`
`(1)/(60)-(10)/(f_1f_2)=(1)/(30)implies(10)/(f_1f_2)=-(1)/(60)`
`f_1f_2=-600,(1)/(f_1)+(1)/(f_2)=(1)/(60)`
`(f_1+f_2)/(f_1f_2)=(1)/(60)implies(f_1+f_2)/(-600)=(1)/(60)`
`f_1+f_2=-10`
`f_1=20cm,f_2=-30cm`