Question

Q4. The image formed by a convex mirror is only one-
third of the size of the object. If the focal length of
the mirror is 12 cm, the image formed will be:
(a) 8 cm behind the mirror
(b) 10 cm behind the mirror
(C) 8 cm in front of the mirror
(d) 10 cm in front of the mirror
​

Answer 1

Image formed by a convex mirror is 1/3 of the object

So Magnification (m) = 1/3

Also Magnification (m) = - v/u

⇒ 1/3 = - v/u

⇒ 3 = - u/v

⇒ 3v = - u

⇒ - 3v = u

⇒ u = - 3v

Focal length (f) = 12 cm

Image distance = v

Object distance (u) = - 3v

We know that

1/f = (1/v) + (1/u)

⇒ 1/12 = (1/v) + (1/-3v)

⇒ 1/12 = (1/v) + (-1/3v)

⇒ 1/12 = (3 - 1)/3v

⇒ 1/12 = 2/3v

⇒ 3v/12 = 2

⇒ v/4 = 2

⇒ v = 2(4)

⇒ v = 8

Since object distance is positive image is formed behind the mirror at a distance of 8 cm.

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