If a lens is moved towards the object from a distance of $40 \,cm$ to $30 \,cm$,the magnification of the image remains the same (numerically). The focal length of the lens is ......... $cm$.

$A$ plano-convex lens is made of a material with a refractive index of $1.6$. The radius of curvature of the curved surface is $60 \ cm$. The focal length of the lens is.....$cm$.

How is it convenient to obtain an image by a lens practically?

The following figure shows a beam of light converging at point $P$. When a concave lens of focal length $16 \,cm$ is introduced in the path of the beam at a place shown by the dotted line such that $OP$ becomes the axis of the lens,the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to (in $\,cm$)

$A$ biconvex lens of refractive index $1.5$ has a focal length of $20 \,cm$ in air. Its focal length when immersed in a liquid of refractive index $1.6$ will be:

$A$ lens is placed between a source of light and a wall. It forms images of area $A_1$ and $A_2$ on the wall for its two different positions. The area of the source of light is