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,when silvered on the plane side,behaves like a concave mirror of focal length $30 \ cm$. However,when silvered on the convex side,it behaves like a concave mirror of focal length $10 \ cm$. The refractive index of its material is:

The plane surface of a plano-convex lens of focal length $f$ is silvered. It will behave as

An object is placed at a distance of $15\;cm$ from a convex lens of focal length $10\;cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. Find the focal length of the convex mirror if the distance between the lens and the mirror is $30\;cm$. (in $;cm$)

$A$ point object is held above a thin equiconvex lens at its focus. The focal length is $0.1 \ m$ and the lens rests on a horizontal thin plane mirror. The final image will be formed at

$A$ 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