g.b

m = 1/2 (since convex mirrors always form virtual images)

u = - 60 cm.

We know,

m = -v/u

=> 1/2 = -v / - 60 => v = 60/2 = 30 cm

Also, according to the mirror formula,

1/f = 1/v + 1/u

=> 1/f = 1/30 - 1/60

=> 1/f = (2-1)/60

=> 1/f = 1/60 => f = 60cm

So, the focal length of mirror is 60 cm.

Now, we are given that m = 1/3

m = -v/u

=> 1/3 = -v/u => v = -u/3

According to mirror formula,

1/f = 1/u + 1/v

=> 1/60 = 1/u - 3/u

=> 1/60 = -2/u

Therefore, u = -2 * 60 = -120 cm

Therefore, required distance of the object to produce a magnification of 1/3 is 120 cm.