Question

An object is kept behind a concave mirror of focal length 20cm.the image is three times the object size. Calculate two possible distances of the object from the mirror.

Answer 1

Given , f= -20
m = +3 or -3 (two different positions)

m = -v/u
3= -v/u
v = -3u. [1]

1/f=1/v+1/u
thus, 1/-20 = 1/-3u + 1/u. ( from 1 replacing v)
1/-20 = 2/3u
​3u = -40. (Cross multiplying)
u= -40/3


Now if m = -3
m = -v/u
-3 = -v/u
v= 3u. [2]

1/f= 1/v + 1/u
1/-20= 1/3u + 1/u. (Replacing v by [2])
1/-20=4/3u
3u = -80
u= -80/3 cm

Thus the two positions are -40/3 cm and -80/3 cm