$A$ real image of an object is formed at a distance of $20 \, cm$ from a lens. On putting another identical lens in contact with it,the image is shifted $10 \, cm$ towards the combination. The power of the lens is (in $, D$)

In which optical instruments is a combination of lenses used?

An eye specialist prescribes 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 lens combination in diopters is

$A$ point object,$O$ is placed in front of two thin symmetrical coaxial convex lenses $L_1$ and $L_2$ with focal lengths $24\,cm$ and $9\,cm$ respectively. The distance between the two lenses is $10\,cm$ and the object is placed $6\,cm$ away from lens $L_1$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is .........$cm$.

An object is placed $30 \ cm$ away from a convex lens of focal length $10 \ cm$ and a sharp image is formed on a screen. Now, a concave lens is placed in contact with the convex lens. The screen now has to be moved by $45 \ cm$ to get a sharp image again. The magnitude of the focal length of the concave lens is (in $cm$):

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. The lenses are made of different materials with refractive indices $n_1$ and $n_2$,and $R$ is the radius of curvature of the curved surfaces. What is the focal length of the combination?