Draw ray diagrams to show the nature, position and relative size of the image formed by a convex mirror when the object is placed (i) at infinity and (ii) between infinity and pole P of the mirror.

Step 1: Understanding the Problem

The problem asks us to draw ray diagrams to show the nature, position, and relative size of the image formed by a convex mirror when the object is placed (i) at infinity and (ii) between infinity and pole P of the mirror.

Step 2: Drawing Ray Diagrams

To solve this problem, we need to draw ray diagrams for the two given scenarios.

Scenario (i): Object at Infinity

When the object is at infinity, the incident rays are parallel to each other. The reflected rays will appear to diverge from the focal point F of the convex mirror.

``diagram {"type": "ray-diagram", "objects": ["convex mirror", "object at infinity"], "rays": ["incident ray 1", "incident ray 2", "reflected ray 1", "reflected ray 2"], "labels": ["F", "P", "C"]}

`

Scenario (ii): Object Between Infinity and Pole P

When the object is between infinity and pole P, the incident rays will be converging. The reflected rays will appear to diverge from a point behind the mirror, forming a virtual image.

`diagram {"type": "ray-diagram", "objects": ["convex mirror", "object between infinity and pole P"], "rays": ["incident ray 1", "incident ray 2", "reflected ray 1", "reflected ray 2"], "labels": ["F", "P", "C"]}

``

Step 3: Analyzing the Images

In both scenarios, the image formed by the convex mirror is virtual, erect, and smaller than the object.

The final answer is: oxed{No specific numerical answer required for this problem.}