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

Find the position of the image formed by the lens combination given in the figure.

$A$ lens of power $+2 \text{ D}$ is placed in contact with a lens of power $-1 \text{ D}$. The combination will behave like:

Three lenses $L_1, L_2, L_3$ are placed co-axially as shown in the figure. The focal lengths of the lenses are $30 \, cm, 10 \, cm$ and $5 \, cm$ respectively. If a parallel beam of light falls on lens $L_1$ and emerges from $L_3$ as a convergent beam such that it converges at the focus of $L_3$,find the distance $d$ between $L_1$ and $L_2$ in $cm$.

Two thin lenses in contact form an achromatic doublet of power $+2 \text{ D}$. The power of the convex lens is $+5 \text{ D}$. What is the ratio of the dispersive powers of the converging and diverging lenses?

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 $f$?