$f_v$ and $f_r$ are the focal lengths of a convex lens for violet and red lights respectively,and $F_v$ and $F_r$ are the magnitudes of the focal lengths of a concave lens for violet and red lights respectively. Then:

$A$ lens forms real and virtual images of an object when the object is at $u_1$ and $u_2$ distances respectively. If the size of the virtual image is double that of the real image,then the focal length of the lens is (Take the magnification of the real image as $m$)

$A$ convex lens is made of $3$ layers of glass of $3$ different materials as shown in the figure. $A$ point object is placed on its axis. The number of images of the object formed is:

For an object placed at a distance $2.4\,m$ from a lens,a sharp focused image is observed on a screen placed at a distance $12\,cm$ from the lens. $A$ glass plate of refractive index $1.5$ and thickness $1\,cm$ is introduced between the lens and the screen such that the glass plate faces are parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen (in $,m$)?

$A$ lens of refractive index $n$ is placed in a liquid of refractive index $n'$. If the focal length of the lens in air is $f$,what will be its focal length in the liquid?

The refractive index of the material of a concave lens is $\mu$. It is immersed in a medium of refractive index $\mu_1$. $A$ parallel beam of light is incident on the lens. The path of the emergent rays when $\mu_1 > \mu$ is