The focal length of a planoconvex glass lens is $20 \,cm$ $(\mu_g=1.5)$. The plane face of it is silvered. An illuminating object is placed at a distance of $60 \,cm$ from the lens on its axis along the convex side. Then the distance (in $cm$) of the image is .........

$A$ point-like object is placed at a distance of $1\, m$ in front of a convex lens of focal length $0.5\, m$. $A$ plane mirror is placed at a distance of $2\, m$ behind the lens. Find the position and nature of the final image formed by the system.

$A$ 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 $cm$?

An equiconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be

$A$ symmetric double convex lens is cut into two equal parts by a plane perpendicular to the principal axis. If the power of the original lens was $4 \ D$,what will be the power of each cut lens (in $D$)?

The diagram shows a silvered equiconvex lens. An object of length $1\,cm$ is placed at a distance of $30\,cm$ in front of the lens. What will be the final image properties? The refractive index of the lens is $\mu$ and the refractive index of the medium in which the lens has been placed is $2\mu$. Both surfaces have a radius of curvature $R$.