The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal lengths $10 \,cm$ and $15 \,cm$ respectively. The distance between $L_1$ and $L_2$ is: (in $\,cm$)

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4:3$. If the effective focal length of the combination is $+60 \ cm$, then the focal lengths of the lenses should be:

$A$ combination of two thin convex lenses of focal lengths $0.3 \, m$ and $0.1 \, m$ will have minimum spherical and chromatic aberrations if the distance between them is . . . . . . $m$.

$A$ convex lens of focal length $20 \, cm$ is cut into two equal parts. This results in two plano-convex lenses as shown in the figure. These two parts are then placed in contact with each other as shown in the figure. What will be the focal length of the system in $cm$?

$A$ 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:

$A$ convex lens has $9 \ cm$ focal length and a concave lens has $-18 \ cm$ focal length. The focal length of the combination in contact will be.....$cm$