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 $\,cm$)

$A$ pin is placed at a distance of $10 \, cm$ in front of a convex lens of focal length $20 \, cm$. The lens is made of a material with a refractive index of $1.5$. The surface of the lens farther from the pin is silvered,and its radius of curvature is $22 \, cm$. Find the position of the final image in $cm$.

$A$ plano-convex lens $(f = 20 \ cm)$ is silvered at the plane surface. Now,the new focal length $F$ will be........$cm$.

$A$ luminous object is placed at a distance of $30 \,cm$ from a convex lens of focal length $20 \,cm$. On the other side of the lens,at what distance from the lens should a convex mirror of radius of curvature $10 \,cm$ be placed in order to have an upright image of the object coincident with it (in $,cm$)?

$A$ planoconvex lens becomes an optical system of $28 \, cm$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig $-A$. If the same lens is instead silvered on the curved surface and illuminated from the other side as in Fig. $-B$, it acts like an optical system of focal length $10 \, cm$. The refractive index of the material of the lens is

$A$ convex lens of focal length $20 \, cm$ and a concave mirror of focal length $f$ are placed coaxially at a distance of $5 \, cm$ apart. $A$ parallel beam of light incident on the convex lens emerges from the system as a parallel beam. Then $f = \dots \, cm$.