Find the linear magnification in the given diagram.

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 $cm$)

$A$ 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.....$cm$.

One plano-convex and one plano-concave lens of same radius of curvature $R$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $\mu_1$ and that of $2$ is $\mu_2$,then the focal length of the combination is

What is the focal length of a convex lens of focal length $30 \, cm$ in contact with a concave lens of focal length $20 \, cm$? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

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 $cm$.