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

Magnification, m=-3

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) For virtual image
m= 3 and f= -15 cm

m=h2 /h1=- v/u=3
v=-3u

Using mirror formula,

1/(-3u) +1/u=1/-15
u=-10 cm
so object should be placed 10 cm from the concave mirror