$A$ convex lens is made of $3$ layers of glass of $3$ different materials as shown in the figure. $A$ point object is placed on its axis. The number of images of the object formed is:

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

$A$ 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:

The magnifications produced by a convex lens for two positions of an object are $4$ and $3$, respectively. If the distance of separation between the two positions of the object is $2 \,cm$, then the focal length of the lens is (in $\,cm$)

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

The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 \,cm$. If the radii of curvature are equal, the value of the radius of curvature (in $cm$) is