$A$ convex lens has a focal length $f$. It is cut into two parts along the dotted line as shown in the figure. The focal length of each part will be

$A$ plano-convex lens $(f=20 \,cm)$ is silvered at its plane surface. What will be its new focal length (in $\,cm$)?

One face of a rectangular glass plate $6 \, cm$ thick is silvered. An object held $8 \, cm$ in front of the first face forms an image $12 \, cm$ behind the silvered face. The refractive index of the glass is

$A$ 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 . . . . . . $\text{cm}$.

$A$ 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,where will the image form?

$A$ 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