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

The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to make the achromatic combination from the two lenses,in $cm$ is

Two lenses of power $+12 \ D$ and $-2 \ D$ are placed in contact. What will be the focal length of the combination in $cm$?

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 $cm$)

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 $f$?

$A$ combination of two thin lenses in contact has a power of $+10 D$. The power reduces to $+6 D$ when the lenses are $0.25 m$ apart. The power of each individual lens is: