$A$ concave lens and a convex lens are arranged as shown in the figure. Find the position of the final image.

$A$ converging lens of focal length $30 \,cm$ is placed in contact with another converging lens of unknown focal length. Then,the possible value for the focal length of the combination is ......... $cm$.

$A$ plano-convex lens of refractive index ${\mu _1}$ and focal length $f_1$ is kept in contact with another plano-concave lens of refractive index ${\mu _2}$ and focal length $f_2$. If the radius of curvature of their spherical faces is $R$ each and $f_1 = 2f_2$,then ${\mu _1}$ and ${\mu _2}$ are related as:

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:

An object $AB$ is placed $15 \text{ cm}$ on the left of a convex lens $P$ of focal length $10 \text{ cm}$. Another convex lens $Q$ is now placed $15 \text{ cm}$ to the right of lens $P$. If the focal length of lens $Q$ is $15 \text{ cm}$, the final image is . . . . . . .

Two lenses have focal lengths $f_1$ and $f_2$ and their dispersive powers are $\omega_1$ and $\omega_2$ respectively. They will together form an achromatic combination if