Figure shows an object AB placed in front of two thin coaxial lenses 1 and 2 with focal lengths 24 cm and 9.0 cm, respectively. The object is 6.0 cm from the lens/and the lens separation is `L=10cm`. Where does the system of two lenses produce an image of the object AB?

Options

A. `+18cm`
B. `-18cm`
C. `+24cm`
D. `-24cm`

Answer

A

Explanation

For first lens `f_(1)=24.0cm`
`u_(1)=6.0cm`
From the lens formula `1/v-1/(u_(1))=1/(f_(1))`
`=1/(f_(1))+1/(u_(1))=1/24=-1/6`
`1/v=(1-4)/24=-3/24`
`implies v=-8cm`
`:.` For second lens
`u_(2)=-8cm+(-10cm)=-18cm`
`f_(2)=9cm`
Again, using lens formula,
`1/(u_(2))-1/(u_(2))=1/(f_(2))`
`implies1/(v_(2))=1/(f_(2))+1/(u_(2))=1/9-1/18`
`=(2-1)/18=1/18`
`impliesv_(2)=48cm`
`:.` Final image will be formed at 18 cm to the right of scond lens.