Two thin lenses whose powers are $+2 \ D$ and $-4 \ D$ respectively are combined. The power of the combination is:

$A$ 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 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:

$A$ combination of two thin lenses with focal lengths $f_1$ and $f_2$ respectively forms an image of a distant object at a distance of $60 \ cm$ when the lenses are in contact. The position of this image shifts by $30 \ cm$ towards the combination when the two lenses are separated by $10 \ cm$. The corresponding values of $f_1$ and $f_2$ are:

The focal length (in $cm$) of a lens with dispersive power $0.45$ that should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to form an achromatic combination is:

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