Two lenses of power $-15 \, D$ and $5 \, D$ are placed in contact with each other. The focal length of this combination will be ....... $cm$.

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:

In the given optical instrument,how can a third lens of the same focal length be inserted to increase the light-collecting efficiency without changing the positions of the object and the image? Calculate the position of that lens.

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4:3$. If the effective focal length of the combination is $+60 \ cm$,then the focal lengths of the lenses should be:

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

$A$ convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is $2/3$. Their equivalent focal length is $30 \, cm$. Their individual focal lengths in $cm$ will be