Is it possible for a lens to act as a convergent lens in one medium and a divergent lens in another?

Give the mathematical expression for the power of a lens.

The figure below shows an object $AB$ placed on the principal axis of a convex lens placed in air. $F_{1}$ and $F_{2}$ are the two foci of the lens. Copy the diagram.
$(i)$ Draw a ray of light starting from $B$ and passing through $O$. Show the same ray after refraction by the lens.
$(ii)$ Draw another ray from $B$ which passes through $F_{2}$ after refraction by the lens.
$(iii)$ Locate the final image formed.
$(iv)$ Is the image real or virtual?

With the help of a ray diagram,show the formation of an image by a convex lens when the object is placed between $F$ and $2F$. Write two characteristics of the image so formed.

Which of the following is the lens formula?

What is the focal length of the objective of an astronomical telescope as compared to that of the eyepiece?