The two lenses of an achromatic doublet should have:

An achromatic convergent lens of focal length $20 \, cm$ is made of two lenses (in contact) of materials having dispersive powers in the ratio of $1 : 2$ and having focal lengths $f_1$ and $f_2$. Which of the following is true?

Two lenses $A$ and $B$ having focal lengths $2.0 \,cm$ and $5.0 \,cm$, respectively, are placed $14 \,cm$ apart. Lens $A$ is placed to the left of lens $B$. An object is placed $3 \,cm$ to the left of lens $A$. The distance of the final image from lens $A$ will be:

Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The combination is equivalent to a single lens of power:

Two lenses of power $+12 \ D$ and $-2 \ D$ are placed in contact. What will be the focal length of the combination in $cm$?

In the given optical instrument,how can a third lens of the same focal length be inserted to increase the light-collecting efficiency without changing the positions of the object and the image? Calculate the position of that lens.