$A$ plano-convex lens has a diameter of $6\, cm$ and a thickness of $3\, mm$ at the center. If the speed of light in the material of the lens is $2 \times 10^{8}\, m/s$,then the focal length of the lens is ..... $cm$.

$A$ lens is placed between a source of light and a wall. It forms images of area $A_1$ and $A_2$ on the wall for its two different positions. The area of the source of light is

$A$ convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, then

$A$ white light is falling on a bi-convex lens. Which of the following options represents the correct qualitative behaviour of the focussing of this light?

$A$ convex lens is used to form a real image of an object on a screen. It is observed that even when the positions of the object and the screen are fixed,there are two positions of the lens that form real images. If the heights of the images are $4 \ cm$ and $9 \ cm$ respectively,the height of the object is.....$cm$.

$A$ concave lens of glass,refractive index $1.5$,has both surfaces of the same radius of curvature $R$. On immersion in a medium of refractive index $1.75$,it will behave as a: