$A$ magnifying glass is made of a combination of lenses with power $+20\,D$ and $-4\,D$. If the least distance of distinct vision is $25\,cm$,calculate the size of an image of an object $2\,cm$ high seen through the magnifying glass. (in $,cm$)

Two identical glass $(\mu_g = 3/2)$ equiconvex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $(\mu_w = 4/3).$ The focal length of the combination is

Find the position of the final image with respect to the rightmost lens formed by the lens combination shown in the figure.

Three lenses of focal lengths $+10 \ cm, -10 \ cm$ and $+30 \ cm$ are placed at distances of $30 \ cm, 35 \ cm$ and $45 \ cm$ respectively from an object. The distance between the object and the final image formed is: (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?

$A$ collimated beam of light of diameter $2 \ mm$ is propagating along the $x$-axis. The beam is required to be expanded into a collimated beam of diameter $14 \ mm$ using a system of two convex lenses. If the first lens has a focal length of $40 \ mm$, then the focal length of the second lens is . . . . . . $mm$.