$A$ 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

$A$ 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 of focal length $f$ is cut into four equal parts and two parts are placed as shown in the figure. The focal length of the system shown in the figure is:

$A$ plano-convex lens $(\mu = 1.5)$ has a radius of curvature of $10 \; cm$. It is silvered on its plane surface. Find the focal length after silvering. (in $; cm$)

An object is placed $0.1 \,m$ in front of a convex lens of focal length $20 \,cm$ made of a material of refractive index $1.5$. The surface of the lens away from the object is silvered. If the radius of curvature of the silvered surface is $22 \,cm$,then the distance of the final image from the silvered surface is (in $\,cm$)

$A$ thin biconvex lens is prepared from glass $(mu = 1.5)$ where both curved surfaces have equal radii of $20 \text{ cm}$ each. The left side surface of the lens is silvered from the outside to make it reflecting. To have the position of the image and the object at the same place,the object should be placed from the lens at a distance of . . . . . . $\text{cm}$.