$A$ 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 . . . . . . $m$.

Four combinations of two thin lenses are given in List-$I$. The radius of curvature of all curved surfaces is $r$ and the refractive index of all lenses is $1.5$. Match lens combinations in List-$I$ with their focal length in List-$II$ and select the correct answer using the code given below the lists.

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:

$A$ convex lens of power $+6 D$ is placed in contact with a concave lens of power $-4 D$. What is the nature and focal length of the combination?

The dispersive powers of two lenses are $0.01$ and $0.02.$ If the focal length of one lens is $+10\, cm$,what should be the focal length of the second lens so that they form an achromatic combination?

Two thin lenses,when in contact,produce a combination of power $+10 \, D$. When they are $0.25 \, m$ apart,the power reduces to $+6 \, D$. The focal lengths of the lenses (in $m$) are