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

Answer

B

Explanation

`(1)/(60)=(1)/(f_(1))+(1)/(f_(2)),` `(1)/(30)=(1)/(f_(1))+(1)/(f_(2))-(10)/(f_(1)f_(2))`
or `(1)/(30)=(1)/(60)-(10)/(f_(1)f_(2))` or `(10)/(f_(1)f_(2))=(1)/(60)-(1)/(30)`
or `(10)/(f_(1)f_(2))=(1-2)/(60)=-(1)/(60)`or `f_(1)f_(2)=-600`
or `f_(2)=(600)/(f_(1))`
From (1) , `(1)/(60)=(1)/(f_(1))+(1)/((-600)/(f_(1)))`
or`(1)/(60)=(1)/(f_(1))-(f_(1))/(60)` or `(1)/(60)=(60-f_(1)^(2))/(600f_(1))`
or `600f_(1)=36000-60f_(2)^(1)`
or `60g_(1)^(2)+600f_(1)-36000=0`
or `f_(1)^(2)+10f_(1)-600=0`
or`f_(1)^(2)+30f_(1)-20f_(1)-600=0`
or `f_(1)(f_(1)+30)-20(f_(1)+30)=0`
`f_(1)=20cm `or `f_(1)=-30cm`
Now, `f_(2)=(600)/(20)cm` or `(-600)/(-30)`
or`f_(2)=-30cm or 20cm`