$A$ convex lens of focal length $20 \, cm$ is cut into two equal parts. This results in two plano-convex lenses as shown in the figure. These two parts are then placed in contact with each other as shown in the figure. What will be the focal length of the system in $cm$?

What is the position and nature of the image formed by the lens combination shown in the figure? ($f_1, f_2$ are focal lengths)

Two lenses of power $-15 \ D$ and $+5 \ D$ are in contact with each other. The focal length of the combination is ....... $cm$.

The lens combination consists of two lenses, $L_1$ and $L_2$, of focal lengths $+10 \text{ cm}$ and $-10 \text{ cm}$, respectively. The object is placed at a distance of $30 \text{ cm}$ from the first lens $L_1$. The distance between the two lenses is $3 \text{ cm}$. Find the position of the final image formed.

Two lenses have focal lengths $f_1$ and $f_2$ and their dispersive powers are $\omega_1$ and $\omega_2$ respectively. They will together form an achromatic combination if

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 $\,m$)