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 diagram below shows an object placed at a distance $2f$ in front of a convex lens of focal length $f$. Which of the following represents the positions of the image when $(i)$ a parallel-sided glass block,or $(ii)$ a converging lens of long focal length is inserted between the object and the convex lens?

$A$ combination of two thin lenses of the same material with focal lengths $f_1$ and $f_2$,arranged on a common axis,minimizes chromatic aberration if the distance between them is:

The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to make the achromatic combination from the two lenses,in $cm$ is

One plano-convex and one plano-concave lens of same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $\mu_1$ and that of $2$ is $\mu_2$,then the focal length of the combination is

Two lenses having focal lengths in the ratio $f_1:f_2 = 2:3$ are combined to produce no net dispersion. Find the ratio of the dispersive powers of the glasses used.