$A$ convergent doublet of separated lenses,corrected for spherical aberration,has a resultant focal length of $10\,cm$. The separation between the two lenses is $2\,cm$. The focal lengths of the component lenses are:

Find the position of the final image with respect to the rightmost lens formed by the lens combination shown in the figure.

$A$ convex and a concave lens separated by a distance are then put in contact. How does the focal length of the combination change?

The ratio of the dispersive powers of two lenses is $4:3$. If the achromatic combination of these two lenses in contact is a convex lens of focal length $60 \, cm$,find the focal lengths of the component lenses.

Two thin plano-convex lenses each of focal length $f$ are placed as shown in the figure. The ratio of their effective focal lengths in the three cases is

The lens combination consists of two lenses, $L_1$ and $L_2$, of focal lengths $+10 \text{ cm}$ and $-10 \text{ cm}$, respectively. The object is placed at a distance of $30 \text{ cm}$ from the first lens $L_1$. The distance between the two lenses is $3 \text{ cm}$. Find the position of the final image formed.