Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The power of the combination is

$A$ thin convex lens of focal length $30 \, cm$ forms an image $2 \, cm$ high,of an object at infinity. $A$ thin concave lens of focal length $20 \, cm$ is placed $26 \, cm$ from the convex lens on the side of the image. The height of the final image is.....$cm$.

Three lenses $L_1, L_2, L_3$ are placed co-axially as shown in the figure. The focal lengths of the lenses are $30 \, cm, 10 \, cm$ and $5 \, cm$ respectively. If a parallel beam of light falls on lens $L_1$ and emerges from $L_3$ as a convergent beam such that it converges at the focus of $L_3$,find the distance $d$ between $L_1$ and $L_2$ in $cm$.

$A$ converging lens of focal length $30 \,cm$ is placed in contact with another converging lens of unknown focal length. Then,the possible value for the focal length of the combination is ......... $cm$.

$A$ 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 . . . . . . $mm$.

The size of the image of an object at infinity, 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, what is the new size of the image (in $\,cm$)?