$A$ convex lens of focal length $1/3 \ m$ forms a real,inverted image twice the size of the object. The distance of the object from the lens is: (in $m$)

In the displacement method,a convex lens forms a real image of an object for its two different positions. If the heights of the images in the two cases are $24 \,cm$ and $6 \,cm$,then the height of the object is ........ $cm$.

Define power of a lens,obtain its equation and write its $SI$ unit.

The figure given below shows a beam of light converging at point $P.$ When a concave lens of focal length $16 \ cm$ is introduced in the path of the beam at a place $O$ shown by the dotted line such that $OP$ becomes the axis of the lens,the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to.....$cm$.

When a biconvex lens of glass having refractive index $1.47$ is dipped in a liquid,it acts as a plane sheet of glass. This implies that the liquid must have a refractive index:

For a concave lens of focal length $f$,the relation between object distance $u$ and image distance $v$ from its pole can best be represented by ($u = v$ is the reference line):