$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a convex lens of focal length $20 \, cm$ (in $, cm$)?

The focal length of a lens with a refractive index of $1.5$ in air is $0.30 \ m$. When it is immersed in a liquid of refractive index $\frac{4}{3}$,its focal length in the liquid will be ...... $cm$.

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

In an experiment to measure the focal length $(f)$ of a convex lens,the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y-x$ plot is shown in the figure. The focal length of the lens is . . . . . . $cm$.

If in a plano-convex lens,the radius of curvature of the convex surface is $10 \ cm$ and the focal length of the lens is $30 \ cm,$ then the refractive index of the material of the lens will be

$A$ lamp is placed $6.0\; m$ from a wall. On putting a lens between the lamp and the wall at a distance of $1.2\; m$ from the lamp,a real image of the lamp is formed on the wall. The magnification of the image is