$A$ concave lens of focal length $20 \ cm$ placed in contact with a plane mirror acts as a

$A$ 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

Two thin similar convex lenses are joined together front to front with the rear portion silvered such that a sharp image of an object at infinity is formed $20 \, cm$ from the mirror. When the air between the lenses is replaced by water $(\mu_w = 4/3)$,then the image formed by the mirror is at a distance of ........ $cm$.

An equiconvex lens is cut into two parts along its $(i) \ XOX'$ axis and $(ii) \ YOY'$ axis as shown in the figure. Let $f, f', f''$ be the focal lengths of the original lens,each half in the first case,and each half in the second case,respectively. Which of the following statements is correct?

The diagram shows a silvered equiconvex lens. An object of length $1\,cm$ is placed at a distance of $30\,cm$ in front of the lens. What will be the final image properties? The refractive index of the lens is $\mu$ and the refractive index of the medium in which the lens has been placed is $2\mu$. Both surfaces have a radius of curvature $R$.

Two identical thin plano-convex glass lenses (refractive index $1.5$) each having a radius of curvature of $20\, cm$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index $1.7$. The focal length of the combination is.......$cm$.