$(a)$ Define principal focus of a spherical mirror.
$(b)$ For what position of the object does a concave mirror form a real,inverted and diminished image of the object? Draw the ray diagram.
$(c)$ An object $4 \,cm$ high is placed at a distance of $6 \,cm$ in front of a concave mirror of focal length $12 \,cm$. Find the position of the image formed.

(C) The principal focus is a point on the principal axis where rays parallel to the principal axis converge (in a concave mirror) or appear to diverge from (in a convex mirror) after reflection.
$(b)$ $A$ concave mirror forms a real,inverted,and diminished image when the object is placed beyond the center of curvature $(C)$.
$(c)$ Given: Object height $h = 4 \,cm$,object distance $u = -6 \,cm$,focal length $f = -12 \,cm$.
Using the mirror formula: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$\frac{1}{-12} = \frac{1}{v} + \frac{1}{-6}$
$\frac{1}{v} = \frac{1}{6} - \frac{1}{12} = \frac{2-1}{12} = \frac{1}{12}$
$v = 12 \,cm$.
The image is formed at a distance of $12 \,cm$ behind the mirror (virtual image).