When an object is at a distance $u_1$ and $u_2$ from a lens,a real image and a virtual image are formed,respectively,having the same magnification $m$. The focal length of the lens is:

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

$A$ substance is behaving as a convex lens in air and a concave lens in water. What is its refractive index?

An object is placed at a certain distance to the left of a convex lens of focal length $20 \,cm$. Find the distance of the object if the image obtained is magnified by $4$ times.

$A$ diminished image of an object is to be obtained on a large screen $1\, m$ from it. This can be achieved by

$A$ plano-convex thin lens is used to obtain the image of a point object $O$ on the screen $S$ as shown in the figure. The thickness of the lens in the middle is $0.5 \ cm$ and the refractive index of the material of the lens is $1.5$. If the separation $D$ between the object and the screen is to be minimum,then the aperture diameter of the lens should be.....$cm$.