Let $u$ and $v$ be the distances of the object and the image from a lens of focal length $f$. The correct graphical representation of $u$ and $v$ for a convex lens when $|u|>f$,is

If a concave lens is placed in the path of converging rays,a real image will be produced if the distance of the pole from the point of convergence of incident rays lies between ($f =$ magnitude of focal length of lens).

$A$ hollow lens is made of thin glass and in the shape of a double concave lens. It can be filled with air,water of refractive index $1.33$,or $CS_2$ of refractive index $1.6$. It will act as a diverging lens,if it is

Consider the following statements regarding the real images formed with a converging lens.
$I$. Real images can be seen only if the image is projected onto the screen.
$II$. The real image can be seen only from the same side of the lens as that on which the object is positioned.
$III$. Real images produced by converging lenses are not only laterally but also longitudinally inverted as with mirrors.
Which of the above statement$(s)$ is/are incorrect?

An object of height $25 \ cm$ is placed in front of a convex lens of focal length $30 \ cm$. If the height of the formed image is $50 \ cm$,then the distance between the object and the image is ..... $cm$.

$A$ glass convex lens has a refractive index of $1.55$ with both faces having the same radius of curvature. What is the radius of curvature required if the focal length is to be $20 \,cm$ (in $\,cm$)?