Question

a convex mirror has a focal length of 20cm find the position of object for which image will be half of the size of the object

Answer 1

Given f=20cm

m=1/2

but,m=-v/u

1/2=-v/u

v=-u/2

1/v=-2/u

We know 1/f=1/u+1/v

=1/20=1/u-2/u

=-1/u=1/20

=u=-20

The answer is 20 cm behind the lens.

Answer 2

Answer:

The Object is 20 cm behind the convex mirror.

Explanation:

Given,

f=20cm

Let,

height of image=x

height of object=x/2

Now,

M=height of image/height of object

M=x/2 × 1/x

M=1/2

Also,

M=-v/u

1/2=-v/u

v=-u/2

We know,

1/f=1/v+1/u

1/20=(-2/u)+1/u

1/20=-1/u

u=-20