When a thin convex lens is placed in contact with a concave mirror of the same focal length,the resultant focal length of the system is ......

$A$ thin convex lens of focal length $25 \, cm$ is cut into two pieces $0.5 \, cm$ above the principal axis. The top part is placed at $(0,0)$ and an object is placed at $(-50 \, cm, 0)$. Find the coordinates of the image.

The figure shows an equiconvex lens of focal length $f$. If the lens is cut along $AB$,the focal length of each half will be

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 $R$.

$A$ 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 $...........\,D$.

$A$ point source of light is placed at $2f$ from a converging lens of focal length $f$. $A$ flat mirror is placed on the other side of the lens at a distance $d$ such that rays reflected from the mirror are parallel after passing through the lens again. If $f=30 \, cm$,then $d$ is equal to ............. $cm$.