$A$ convex lens of focal length $15 \,cm$ is placed in front of a plane mirror at a distance of $25 \,cm$ from the mirror. Where on the optical axis and from the centre of the lens should a small object be placed such that the final image coincides with the object?

$A$ converging mirror is placed on the right-hand side of a converging lens as shown in the figure. The focal length of the lens and the mirror are $15 \ cm$ and $20 \ cm$ respectively. The separation between the lens and the mirror is $40 \ cm$ and their principal axes coincide. $A$ point source is placed on the principal axis at a distance $d$ to the left of the lens. If the final beam comes out parallel to the principal axis, then the value of $d$ is: (in $cm$)

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 $;cm$)

The final image of the object forms on the object itself. If the focal length of the lens is $30 \ cm$,then the radius of curvature of the mirror is .... $cm$.

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?

Given is a thin convex lens of glass (refractive index $\mu$) and each side having radius of curvature $R$. One side is polished for complete reflection. At what distance from the lens,an object be placed on the optic axis so that the image gets formed on the object itself?