Two thin convex lenses of focal lengths $20 \; cm$ and $25 \; cm$ are placed in contact. The effective power of the 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 $cm$)

$A$ 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 . . . . . .

An object $AB$ is placed $15 \text{ cm}$ on the left of a convex lens $P$ of focal length $10 \text{ cm}$. Another convex lens $Q$ is now placed $15 \text{ cm}$ to the right of lens $P$. If the focal length of lens $Q$ is $15 \text{ cm}$, the final image is . . . . . . .

Two thin lenses,when in contact,produce a combination of power $+10 \, D$. When they are $0.25 \, m$ apart,the power reduces to $+6 \, D$. The focal lengths of the lenses (in $m$) are

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)