Question

the radius of curvature of a convex mirror is 20 CM the size of the image formed is half of the size of the object find the distance of the object and image

Answer 1

Radius of curvature = 20cm
 so, focal length = 10cm

We are given, ho/2 = hi
                      so, ho= 2hi
                     so, m = hi/ho
                           m = ho/2ho
                           m = 1/2

so, m = -v/u
     1/2 = -v/u
so, u = -2v

By mirror formula,

1/f = 1/v+1/u
 1/10 =  1/v -(-1/2v)
 1/10 = 1/v+1/2v
 so, 1/10 = 2+1/2v
  so, 1/10 = 3/2v
 so, 2v = 30
 so, v = 15 cm 

so, position of object, u  = -2(v) = -30 

Answer 2

Answer:

I hope it helps

Explanation:

Radius of curvature = 20cm

so, focal length = 10cm

We are given, ho/2 = hi

                     so, ho= 2hi

                    so, m = hi/ho

                          m = ho/2ho

                          m = 1/2

so, m = -v/u

    1/2 = -v/u

so, u = -2v

By mirror formula,

1/f = 1/v+1/u

1/10 =  1/v -(-1/2v)

1/10 = 1/v+1/2v

so, 1/10 = 2+1/2v

 so, 1/10 = 3/2v

so, 2v = 30

so, v = 15 cm  

so, position of object, u  = -2(v) = -30