When an object is placed 20cm from a concave mirror , a real image magnified three times is formed. Find:

(a) focal length of the mirror.

(b) where must the object be placed to give a virtual image three times the height of the object?

(a)
Magnification, m=-3 (Image is real)
Object distance, u=-20cm
Magnification, m=-v/u
-3=- v/(-20)
v=-60 cm
Thus the image is located at a distance of 60cm in front of the mirror.
Now using the mirror formula,
1/v +1/u=1/f
1/(-60) + 1/(-20)=1/f
f=-15 cm
(b)
m=h2 /h1=- v/u=3
v=-3u
Using mirror formula,
1/(-3u) +1/u=1/-15
u=-10 cm