A concave mirror is used for image formation for different positions of an object. What inferences can be drawn about the following when an object is placed at a distance of $10\text{ cm}$ from the pole of a concave mirror of focal length $15\text{ cm}$?

(a) Position of the image

(b) Size of the image

(c) Nature of the image

Draw a labelled ray diagram to justify your inferences.

When an object is placed at a distance of $10\text{ cm}$ from a concave mirror of focal length $15\text{ cm}$, the object lies between the pole ($P$) and the principal focus ($F$) of the mirror (since $u < f$).

Based on the principles of reflection and Table 9.1 of the NCERT textbook, the inferences are:

(a) Position of the image: Behind the mirror (at a distance of $30\text{ cm}$ from the pole).

(b) Size of the image: Enlarged (magnified by a factor of $3$).

(c) Nature of the image: Virtual and erect.

Ray Diagram:

``

M

|\

A | \ A'

	\
	\

------B-------P----F'-B'------ (Principal Axis)

C F | /

| /

N/

``

(In this diagram, the object $AB$ is placed between $P$ and $F$. Ray 1 parallel to the principal axis reflects through $F$. Ray 2 passing through $C$ reflects back along $C$. When produced backwards, these rays meet at $A'$ behind the mirror to form the virtual, erect, and enlarged image $A'B'$.)