Question

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

Answer 1

In case of concave mirror

f=-20cm

As specific denotion
h2=1/3 h1

h2/h1=1/3=m
m=-v/u=1/3
v=-1/3u

applying mirror formula

1/f=1/v+1/u

1/-20=-3u/1+1/u

-1/20=-3u²+1 

-u=-60u²+20
60u²-u-20=0

solve this equation by using quadratic equation, the answer will be

u=71/120
u=69/120

Answer 2

Answer.

Here, it is not given whether the lens is concave of convex. So, we will do calculations for both types of mirror.

For concave mirror:

Focal length, f = ‒ 20 cm

Magnification, m = −1/3

Since, magnification, m = − v/u

Magnification, m = −1/3 = − v/u

⟹ v = u/3

Hence, object must be placed at a distance 40 cm from the pole of convex mirror to form erect , virtual, and diminished image.