An optician makes spectacles having a combination of a convex lens of focal length $40 \ cm$ in contact with a concave lens of focal length $25 \ cm$. The power of this combination of lenses in dioptre is:

Two convex lenses ($L_1$ and $L_2$) of equal focal length $f$ are placed at a distance $\frac{f}{2}$ apart. An object is placed at a distance $4f$ to the left of $L_1$ as shown in the figure. The final image is at:

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

An object is located $4 \ m$ from the first of two thin converging lenses of focal lengths $2 \ m$ and $1 \ m,$ respectively. The lenses are separated by $3 \ m$. The final image formed by the second lens is located from the source at a distance of (in $m$):

An optical device is constructed by fixing three identical convex lenses of focal lengths $10 \,cm$ each inside a hollow tube at equal spacing of $30 \,cm$ each. One end of the device is placed $10 \,cm$ away from a point source. What is the image shift in $cm$ when the device is moved away from the source by another $10 \,cm$?

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