$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave mirror of focal length $20 \ cm$. What is the focal length of the system in $cm$?

$A$ biconvex lens of focal length $15 \,cm$ is in front of a plane mirror. The distance between the lens and the mirror is $10 \,cm$. $A$ small object is kept at a distance of $30 \,cm$ from the lens. The final image is

An equiconvex lens is cut into two parts along its $(i) \ XOX'$ axis and $(ii) \ YOY'$ axis as shown in the figure. Let $f, f', f''$ be the focal lengths of the original lens,each half in the first case,and each half in the second case,respectively. Which of the following statements is correct?

An equiconvex lens of focal length $F$ is cut into two equal parts along the vertical axis. The focal length of each part will be

$A$ bi-convex lens of focal length $10\,cm$ is cut into two identical parts along a plane perpendicular to the principal axis. The power of each lens after the cut is $...........\,D$.

An object is placed at a distance of $15\;cm$ from a convex lens of focal length $10\;cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. Find the focal length of the convex mirror if the distance between the lens and the mirror is $30\;cm$. (in $;cm$)