$A$ convex lens of focal length $25 \ cm$ and a concave lens of focal length $10 \ cm$ are joined together. The power of the combination will be

Two thin convex lenses of focal length $f_1$ and $f_2$ are placed in contact with each other. The equivalent power of the lens combination is . . . . . . .

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length $30\,cm$ is $2\,cm$. If a concave lens of focal length $20\,cm$ is placed between the convex lens and the image at a distance of $26\,cm$ from the convex lens, calculate the new size of the image. (in $cm$)

Two lenses of focal lengths $f_1$ and $f_2$ are placed in contact,and the image is formed at a distance of $60 \, cm$. When the lenses are separated by a distance of $10 \, cm$,the image is formed at a distance of $30 \, cm$. What are the values of $f_1$ and $f_2$?

An achromatic convergent doublet of two lenses in contact has a power $+2 \text{ D}$. The convex lens has power $+5 \text{ D}$. The ratio of the dispersive powers of the convergent and divergent lenses is (in magnitude)

Two thin equiconvex lenses each of focal length $0.2 \,m$ are placed coaxially with their optic centres $0.5 \,m$ apart. Then the focal length of the combination is (in $\,m$)