Two lenses of power $3\,D$ and $-5\,D$ are combined to form a compound lens. An object is placed at a distance of $50\,cm$ from this combination. At what distance (in $cm$) will the image be formed?

Find the resultant focal length for the following system where the common radius of curvature is $15 \ cm$. The glass has a refractive index of $1.5$ and water has a refractive index of $\frac{4}{3}$.

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 $f$?

$A$ plano-convex lens (focal length $f_2,$ refractive index $\mu_2,$ radius of curvature $R$) fits exactly into a plano-concave lens (focal length $f_1,$ refractive index $\mu_1,$ radius of curvature $R$). Their plane surfaces are parallel to each other. Then,the focal length of the combination will be

Two lenses $A$ and $B$ having focal lengths $2.0 \,cm$ and $5.0 \,cm$, respectively, are placed $14 \,cm$ apart. Lens $A$ is placed to the left of lens $B$. An object is placed $3 \,cm$ to the left of lens $A$. The distance of the final image from lens $A$ will be:

$A$ convex lens $A$ of focal length $20 \,cm$ and a concave lens $B$ of focal length $56 \,cm$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam, then the magnitude of distance $d$ (in $cm$) is