Question

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 ?

Answer 1

(a) Given for the real image
Magnification, m=-3
Object distance, u=-20cm
Magnification, m=−v/u
−3=−v/(−20)
v=−60cm
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=−15cm
(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=−10cm
so object should be placed 10 cm from the concave mirror