$A$ student wants to project the image of a candle flame on a screen $60\, cm$ in front of a mirror by keeping the flame at a distance of $15\, cm$ from its pole.
$(a)$ Write the type of mirror he should use.
$(b)$ Find the linear magnification of the image produced.
$(c)$ What is the distance between the object and its image?
$(d)$ Draw a ray diagram to show the image formation in this case.

(A) Since the image is formed on a screen,it must be a real image. Only a concave mirror can form a real image.
$(b)$ Given: Object distance $u = -15\, cm$,Image distance $v = -60\, cm$ (as it is in front of the mirror).
Linear magnification $m = \frac{v}{u} = \frac{-60}{-15} = -4$.
$(c)$ The object is at $15\, cm$ from the pole and the image is at $60\, cm$ from the pole on the same side.
Distance between object and image $= |v - u| = |-60 - (-15)| = |-60 + 15| = |-45| = 45\, cm$.
$(d)$ The ray diagram shows the object placed between the focus $F$ and the pole $P$ is incorrect based on the values; however,for a real image,the object must be placed between $C$ and $F$. The provided diagram shows the object between $C$ and $F$ forming a real,inverted,and magnified image beyond $C$.