The following graph depicts the inverse of magnification $(1/m)$ versus the distance between the object and the lens $(u)$ for a setup. The focal length of the lens used in the setup is .................... $m$.

An equiconvex lens is cut into two halves along $(i) XOX'$ and $(ii) YOY'$ as shown in the figure. Let $f, f', f''$ be the focal lengths of the complete lens,of each half in case $(i),$ and of each half in case $(ii),$ respectively. Choose the correct statement from the following:

An object is placed at a distance of $4\,cm$ in front of a concave lens of focal length $12\,cm$. The nature and position of the image from the lens is

$A$ convex lens of focal length $20 \ cm$ produces images of the same magnification $2$ when an object is kept at two distances $x_1$ and $x_2$ $(x_1 > x_2)$ from the lens. The ratio of $x_1$ and $x_2$ is

$A$ screen is placed $90 \, cm$ from an object. The image of the object is formed on the screen by a convex lens at two different locations separated by $20 \, cm$. If the sizes of the images formed at these positions are $6 \, cm$ and $3 \, cm$,then the height of the object is.....$cm$.

An achromatic combination is made with a lens of focal length $f$ and dispersive power $\omega$ with a lens having a dispersive power of $2\omega$. The focal length of the second lens will be: