If the focal lengths of a lens for red and violet light rays are $f_{R}$ and $f_{V}$ respectively,then which of the following is the true relationship?

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 figure shows a convex lens cut symmetrically into two equal halves and separated laterally by a distance $h$. $A$ point object placed at a distance $30\, cm$ from the lens halves forms two real images separated by a distance $d$. $A$ plot of $d$ versus $h$ is shown in the figure. The focal length of the lens is ......$cm$.

$A$ 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 $, cm$)?

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

The minimum distance between an object and its real image formed by a convex lens is