Two identical symmetric double convex lenses of focal length $f$ are cut into two equal parts $L_1, L_2$ by the $AB$ plane and $L_3, L_4$ by the $XY$ plane as shown in the figure respectively. The ratio of the focal lengths of lenses $L_1$ and $L_3$ is

$A$ thin plano-convex lens made of glass of refractive index $1.5$ is immersed in a liquid of refractive index $1.2$. When the plane side of the lens is silver-coated for complete reflection,the lens immersed in the liquid behaves like a concave mirror of focal length $0.2 \ m$. The radius of curvature of the curved surface of the lens is: (in $m$)

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

$A$ plano-convex lens,when silvered at its plane surface,is equivalent to a concave mirror of focal length $28 \, cm$. When its curved surface is silvered and the plane surface is not silvered,it is equivalent to a concave mirror of focal length $10 \, cm$. Find the refractive index of the material of the lens.

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 $\,cm$)

The distance between a convex lens and a plane mirror is $10 \, cm$. The parallel rays incident on the convex lens after reflection from the mirror form an image at the optical centre of the lens. The focal length of the lens will be.....$cm$.