The size of the image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3 rd to its size. At what distance, the object has been placed from the mirror?

The size of the image of an object by a mirror having a focal length of

20 cm

is observed to be reduced to

1 / 3

rd to its size. The object is placed at a distance of

- 80 cm

from the concave mirror and a distance of

- 40 cm

from the convex mirror.
A diminished image is formed in both concave and convex mirrors.
For concave mirrors:
It is given that the focal length

f = - 20 cm

and magnification

m = - 1 / 3

.
Now, the object distance

u

is given by,

= > m = - v / u

= > - 1 / 3 = - v / u

= > v = u / 3

Using the mirror formula,

1 / f = 1 / v + 1 / u

= > 1 / f = 1 / u + 3 / u

= > u = 4 f

= > u = - 80 cm

Hence, the object distance is

- 80 cm

from the concave mirror.
For convex mirrors:
It is given that the focal length

f = 20 cm

and magnification

m = 1 / 3

.
Now, the object distance ‘u; is given by,

= > m = - v / u

= > 1 / 3 = - v / u

= > v = - u / 3

Using the mirror formula,

1 / f = 1 / v - 1 / u

= > 1 / f = 1 / u - 3 / u

= > u = - 2 f

= > u = - 40 cm

Hence, the object distance is

- 40 cm

The size of the image of an object by a mirror having a focal length of $20 cm$ is observed to be reduced to $1 / 3$ rd to its size. At what distance, the object has been placed from the mirror?