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

When an object is placed at the center of curvature $(C)$ in front of a concave mirror,what kind of image is formed?

Define absolute refractive index. Absolute refractive indices of medium $A$ and medium $B$ are $n_{a}$ and $n_{b}$ respectively. What is the refractive index of medium $B$ with respect to medium $A$? How does the velocity of light vary with change in the optical density of the media?

What is the absolute refractive index of common glass?

$A$ convex lens has a focal length of $25\, cm$. Calculate the distance of the object from the lens if the image is to be formed on the opposite side of the lens at a distance of $75\, cm$ from the lens. What will be the nature of the image?

$A$ convex lens of focal length $20 \, cm$ can produce a magnified virtual as well as real image. Is this a correct statement? If yes,where shall the object be placed in each case for obtaining these images?