$A$ 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 $m$)

The relation between $n_1$ and $n_2$,if the behavior of light rays is as shown in the figure,is:

$A$ student measures the focal length of a convex lens by placing an object pin at a distance '$u$' from the lens and measuring the distance '$v$' of the image pin. The graph between '$u$' and '$v$' plotted by the student should look like:

$A$ lens of refractive index $n$ is placed in a liquid of refractive index $n'$. If the focal length of the lens in air is $f$,what will be its focal length in the liquid?

The magnification of an object placed in front of a convex lens of focal length $20 \, cm$ is $+2$. To obtain a magnification of $-2$,the object has to be moved a distance equal to.....$cm$

$A$ convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis,the number of images formed are