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

Answer

B

Explanation

`(1)/(60)=(1)/(f_(1))+(1)/(f_(2))` (i)
and `(1)/(30)=(1)/(f_(1))+(1)/(f_(2))-(10)/(f_(1)f_(2))` (ii)
On solving (i) and (ii) `f_(1)f_(2)=-600` and `f_(1)+f_(2)=-10`
Hence`f_(1)=20cm` and `f_(2)= -30cm`