Question

Find the position of an object which when placed in front of a convex mirror produces a virtual image, which is half of the size of the object .

Answer 1

Question is incomplete you did not give value of focal length of convex mirror

Magnification = -v/u

Virtual image is formed so v and u will be of opposite sign

Size of image is 1/2 of the size of object so magnification = 1/2

1/2 = -v/u

v = -u/2

apply mirror formula

1/f = 1/v + 1/u

put v = -u/2

1/f = -2/u + 1/u

so 1/f = -1/u

u = -f

You did not give focal length value object will placed at focal length of the mirror

So answer = -f