Two thin lenses having $R_1$ and $R_2$ as the radii of curvature of their surfaces are kept coaxially together. Their power is proportional to

$A$ plane wave passes through a convex lens. The geometrical shape of the wavefront that emerges is

$A$ convex lens of focal length $30 \,cm$ produces $5$ times magnified real image of an object. What is the object distance (in $\,cm$)?

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.

$A$ student measures the focal length of a convex lens by obtaining an image of an object pin at a distance '$v$' from the lens,with the object placed at a distance '$u$' from the lens. What will the graph between '$u$' and '$v$' look like?

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: