What is the power of the combination of a convex lens and a concave lens of equal focal length $25 \text{ cm}$?

$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave lens of focal length $20 \ cm$. An object is placed at $20 \ cm$ to the left of this lens system. The distance of the image from the lens in $cm$ is . . . . . .

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 combination of lenses produces

$A$ biconvex glass lens has a focal length $f$ and power $P$. It is cut into two symmetric parts along its principal axis. If these two parts are joined as shown in figure $(b)$,what is the new power of the combination?

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)