In order to obtain a real image of magnification $2$ using a converging lens of focal length $20 \ cm,$ where should an object be placed in $cm$?

$A$ point source of light is moving at a rate of $2 \,cm \,s^{-1}$ towards a thin convex lens of focal length $10 \,cm$ along its optical axis. When the source is $15 \,cm$ away from the lens,the image is moving at:

$A$ double convex lens of focal length $20 \ cm$ is made of glass of refractive index $3/2$. When placed completely in water $(_{a}\mu_{w} = 4/3)$,its focal length will be.....$cm$.

The refractive index of a glass convex lens is $1.5$. The radius of curvature of each of the two surfaces of the lens is $40 \ cm$. The ratio of the power of the lens when immersed in a liquid of refractive index $1.25$ to that when placed in air is:

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 $30 \,cm$,the refractive index of the material of the lens will be ..........

The distance $v$ of the real image formed by a convex lens is measured for various object distances $u$. $A$ graph is plotted between $v$ and $u$. Which one of the following graphs is correct?