The graph between $u$ and $v$ for a convex mirror is
(A)

(B)

(C)

(D)

Hint: In this solution, we will use the set known object and image positions for a convex mirror. A convex mirror has a positive focal length which means for rays coming from infinity, the image will be formed on the other side of the mirror.

Complete step by step answer:
Let us start by writing down the cases for a convex mirror for a certain object and image distance.
-When the object is at infinity with respect to the mirror, the image will be formed on the other side of the mirror at an image distance equal to the focal length of the mirror.
-When the object is at a distance equal to twice the focal length of the mirror, the image will be formed at a distance equal to twice the focal length on the other side of the mirror.
-When the object is at the focal length of the mirror, the image formed will be at infinity. With these results in mind, we can see that as we decrease the object distance, the image distance increases.
This behavior is shown in graph (A) hence it is the correct choice.

Note: The relation of object and image distance that we derived above is only valid for object distance as low as the focal length of the lens. For even lower object distances, the image will be formed on the same side as the object for a convex lens. We don’t need to search for exact image and object distances in the graphs but rather look at the general trend of the distances keeping in mind all the cases of object distances.