$A$ plano-convex lens of refractive index $1.5$ and radius of curvature $30 \ cm$ is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens should an object be placed in order to have a real image of the same size as the object? $(... \ cm)$

$A$ 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

$A$ convex lens forms a real image of a point object at a distance of $50 \, cm$ from the convex lens. $A$ concave lens is placed $10 \, cm$ behind the convex lens on the image side. On placing a plane mirror on the image side and facing the concave lens,it is observed that the final image now coincides with the object itself. The focal length of the concave lens is .............. $cm$.

$A$ point object is placed at a distance of $20 \ cm$ from a thin plano-convex lens of focal length $15 \ cm$. If the plane surface is silvered,then the image formed is:

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

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