Size of image of an object by a mirror having a focal length of `20 cm` is observed to be reduced to `1/3rd` of the size ? At what distance the object has been placed from the mirror ? What is the nature of the image and the mirror ?

Explanation

We have to do calculations for both concave and convex mirror as the type of mirror is not specified here.
For concave mirror:
Focal length, f = - 20 cm
Magnification, m = - 1/3
Since, magnification, m = -v/u
Magnification, m = -1/3 = -v/u
`implies v=u//3`
By mirror formula
`1/f = 1/v + 1/u`
`1/f=3/u+1/u=4/u implies u=4f`
= 4(-20)= -80 cm
The placement of object should be at 80 cm in front of the concave mirror.
For convex mirror:
Focal length, f= + 20 cm
Magnification, m = +1/3
Since, magnification, m = -v/u
Magnification, m = 1/3 = -v/u
By mirror formula
`1/f = 1/v + 1/u`
`1/f=(-3)/(u)+1/u=(-2)/(u) implies -2f`
= -2(20) = -40 cm
The placement of object should be at 40 cm in front of the concave mirror, to get a diminished, virtual and erect image.