$A$ convex lens of focal length $30 \ cm$ and a concave lens of $10 \ cm$ focal length are placed so as to have the same axis. If a parallel beam of light falling on the convex lens leaves the concave lens as a parallel beam,then the distance between the two lenses will be.......$cm$.

Two identical equiconvex lenses,each of focal length $f$,are placed side by side in contact with each other with a layer of water in between them as shown in the figure. If the refractive index of the material of the lenses is greater than that of water,how is the combined focal length $F$ related to $f$?

Curved surfaces of a plano-convex lens of refractive index $\mu_{1}$ and a plano-concave lens of refractive index $\mu_{2}$ have equal radius of curvature as shown in the figure. Find the ratio of the radius of curvature to the focal length of the combined lenses.

$(a)$ Determine the 'effective focal length' of the combination of two lenses,a convex lens of focal length $30 \; cm$ and a concave lens of focal length $20 \; cm$,if they are placed $8.0 \; cm$ apart with their principal axes coincident. Does the answer depend on which side of the combination a beam of parallel light is incident? Is the notion of effective focal length of this system useful at all?
$(b)$ An object $1.5 \; cm$ in size is placed on the side of the convex lens in the arrangement $(a)$ above. The distance between the object and the convex lens is $40 \; cm$. Determine the magnification produced by the two-lens system,and the size of the image.

Two thin lenses whose powers are $+2 \ D$ and $-4 \ D$ respectively are combined. The power of the combination is:

An effective power of a combination of $5$ identical convex lenses which are kept in contact along the principal axis is $25 \ D$. Focal length of each of the convex lens is: (in $cm$)