$(a)$ $A$ concave mirror produces a three times enlarged real image of an object placed at $10\, cm$ in front of it. Calculate the focal length of the mirror.
$(b)$ Show the formation of the image with the help of a ray diagram when an object is placed $6\, cm$ away from the pole of a convex mirror.

(N/A) Given: Magnification $m = -3$ (for a real image),Object distance $u = -10\, cm$. We need to find the focal length $f$.
Using the magnification formula: $m = -v/u$
$-3 = -v / (-10)$
$-3 = v / 10$
$v = -30\, cm$
Using the mirror formula: $1/f = 1/v + 1/u$
$1/f = 1/(-30) + 1/(-10)$
$1/f = (-1 - 3) / 30 = -4 / 30$
$f = -30 / 4 = -7.5\, cm$
Thus,the focal length of the concave mirror is $-7.5\, cm$.
$(b)$ The ray diagram for an object placed $6\, cm$ in front of a convex mirror is shown below.