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 figure shows an equiconvex lens (of refractive index $1.50$) in contact with a liquid layer on top of a plane mirror. $A$ small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be $45.0 \; cm$. The liquid is removed and the experiment is repeated. The new distance is measured to be $30.0 \; cm$. What is the refractive index of the liquid?

In an experiment,a convex lens of focal length $15 \, cm$ is placed coaxially on an optical bench in front of a convex mirror at a distance of $5 \, cm$ from it. It is found that an object and its image coincide if the object is placed at a distance of $20 \, cm$ from the lens. The focal length of the convex mirror is.......$cm$.

$A$ plano-convex lens of focal length $30\,cm$ has its plane surface silvered. An object is placed $40\,cm$ from the lens on the convex side. The distance of the image from the lens is.......$cm$

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

When the plane surface of a plano-convex lens is silvered,it behaves as a concave mirror of focal length $60 \ cm$. However,when the convex surface is silvered,it behaves as a concave mirror of focal length $20 \ cm$. What is the refractive index of the lens?