The radius of curvature of the curved face of a plano-convex lens is $12 \,cm$ and its refractive index is $1.5$. Then,the focal length of the lens is (in $\,cm$)

Two objects $P$ and $Q$ are placed at $10 \ cm$ and $30 \ cm$ in front of a convex lens of focal length $20 \ cm$. The correct option for the image of $P$ and $Q$ is:

The sun subtends an angle of $(1/2)^o$ at the surface of the earth. $A$ converging lens of focal length $100\, cm$ is used to obtain an image of the sun on a screen. The diameter of the image formed is about.....$mm$.

$A$ convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black,the image will

In many experimental set-ups,the source and screen are fixed at a distance $D$ and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points.

$A$ convex lens produces a real image $m$ times the size of the object. What will be the distance of the object from the lens?