Question

A`20cm` convex lens is placed in contact with a diverting lens of unknown focal length ,The lens combination acts as a converging lens and has a length of`30cm`.What is the focal length of the diverging lens.

Answer 1

Let`f_(2)`is the length of the diverging lens .Then,
`(1)/(f)=(1)/(f_(1))+(1)/(f_(1))`
it is given that `f_(1)=+20cm,f=30cm`
or`(1)/(30)=(1)/(20)+(1)/(f_(2))`
or`(1)/(f_(2))=(1)/(30)-(1)/(20)=(2-3)/(60)=-(1)/(60)`
Thus`f_(2)=-60cm`
Comment If we change the question and claim that the combination acts as a diverging lens and has a focal length of`30cm`then,
`f_(1)=+20cm,f_(2)=?,f_(3)=-30cm`
`-(1)/(30)=(1)/(20)+(1)/(f_(2))`
`(1)/(f_(2))=-(1)/(30)-(1)/(20)=-(5)/(60)`
`f_(2)=-12cm`