An achromatic combination of lenses is formed by joining

$A$ convex lens of focal length $f$ is cut along the dashed line as shown in the figure. What is the focal length of each part?

$A$ point object,$O$ is placed in front of two thin symmetrical coaxial convex lenses $L_1$ and $L_2$ with focal lengths $24\,cm$ and $9\,cm$ respectively. The distance between the two lenses is $10\,cm$ and the object is placed $6\,cm$ away from lens $L_1$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is .........$cm$.

Find the position of the final image formed by the combination of the three lenses shown in the figure. The focal lengths are $f_1 = 10 \ cm$,$f_2 = -10 \ cm$,and $f_3 = 30 \ cm$.

$A$ thin convex lens of focal length $5 \ cm$ and a thin concave lens of focal length $4 \ cm$ are combined together (without any gap) and this combination has magnification $m_1$,when an object is placed $10 \ cm$ before the convex lens. Keeping the positions of the convex lens and object undisturbed,a gap of $1 \ cm$ is introduced between the lenses by moving the concave lens away,which leads to a change in the magnification of the total lens system to $m_2$. The value of $\left|\frac{m_1}{m_2}\right|$ is . . . . . . .

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