$A$ convex lens of refractive index $1.5$ and focal length $18 \, cm$ in air is immersed in water. The change in focal length of the lens will be $........... \, cm$. (Given refractive index of water $= 4/3$)

An object is placed at a distance $x$ from the focus of a convex lens,and its image is formed at a distance $x'$ from the other focus,as shown in the figure. Which relation do the distances $x$ and $x'$ satisfy?

The radii of curvature of both surfaces of a convex lens of focal length $f$ and focal power $P$ are equal. One of the surfaces is made plane by grinding. The new focal length and focal power of the lens are respectively:

$A$ lens made up of different materials forms two images of a point object $O$ as shown in the figure. Then:

Define power of a lens and write the $SI$ unit of power.

In the displacement method,there are two positions of a lens for which we get a clear image on a screen. If the first position of the lens is at $40 \, cm$ from the object and the second position is at $80 \, cm$ from the object,the focal length of the lens is ......... $cm$.