$(a)$ To construct a ray diagram, we use two rays chosen such that their directions after reflection from the mirror are easily determined. List two such rays and state the path of these rays after reflection for a concave mirror. Use these two rays to draw a ray diagram to locate the image of an object placed between the pole and the focus of a concave mirror.
$(b)$ $A$ concave mirror produces a three-times magnified image on a screen. If the object is placed $20 \text{ cm}$ in front of the mirror, how far is the screen from the object?

(N/A) Two light rays whose paths after reflection are easily known are:
$(i)$ $A$ ray passing through the centre of curvature $(C)$: A light ray passing through the centre of curvature of a concave mirror is reflected back along the same path because it strikes the mirror surface normally (at an angle of incidence $i = 0^\circ$).
(ii) $A$ ray incident obliquely to the principal axis at the pole $(P)$: A ray incident at the pole is reflected obliquely, making equal angles with the principal axis (following the laws of reflection, $\angle i = \angle r$).
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$(b)$ Given:
Magnification $m = -3$ (since the image is formed on a screen, it must be real and inverted).
Object distance $u = -20 \text{ cm}$.
Using the magnification formula $m = -\frac{v}{u}$:
$-3 = -\frac{v}{-20 \text{ cm}}$
$-3 = \frac{v}{20 \text{ cm}}$
$v = -60 \text{ cm}$.
The image is formed $60 \text{ cm}$ in front of the mirror.
The distance between the object and the screen is $|v - u| = |-60 \text{ cm} - (-20 \text{ cm})| = |-40 \text{ cm}| = 40 \text{ cm}$.
The screen is $40 \text{ cm}$ away from the object.