$A$ convex lens of radii of curvature $6 \ cm$ and $12 \ cm$ is immersed in a liquid of refractive index $1.3$. If the refractive index of the material of the lens is $1.5$, then the focal length of the lens when immersed in the liquid is (in $cm$)

An object approaches a convergent lens from the left of the lens with a uniform speed $5 \ m/s$ and stops at the focus. The image:

The figure shows a convex lens cut symmetrically into two equal halves and separated laterally by a distance $h$. $A$ point object placed at a distance $30\, cm$ from the lens halves forms two real images separated by a distance $d$. $A$ plot of $d$ versus $h$ is shown in the figure. The focal length of the lens is ......$cm$.

$A$ film projector magnifies a film onto a screen of area $100 \, cm^2$. If the linear magnification is $4$,what will be the area of the image on the screen in $cm^2$?

$A$ convex lens of focal length $f$ is placed somewhere in between an object and a screen. The distance between the object and the screen is $x$. If the numerical value of the magnification produced by the lens is $m$, then the focal length of the lens is

The optical axis of a thin equiconvex lens is the $x$-axis. The coordinates of the object and its image are $(-40 \, cm, 1 \, cm)$ and $(50 \, cm, -2 \, cm)$ respectively. Find the position of the lens.