Q10) Sire of image of an object formed by a minror hawing a focal length of \( 20 cm \), is objerwed to he rudiued one - phird of its sise. At what distame obyit has luen plaud from the minrors? what is the nature of imaje and the muror?

Question

Q10) Size of image of an object formed by a miror having a focal length of \( 20 cm \), is observed to he ruduced one - third of its size. At what distance object has been placed from the mirror? what is the nature of image and the mirror?

Answer 1

Given, focal length f = 20 cm

Magnification, m = 1/3

We have to find the distance of the object from the mirror.

Since the value of m is positive, the image is virtual and erect.

This implies that the mirror is a convex mirror.

We know, m = -(v/u)

1/3 = -v/u

v = -u/3

Using the mirror formula,

1/f = 1/v + 1/u

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

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

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

1/20 = -2/u

u = -2(20)

u = -40 cm

Therefore, the required object distance is 40 cm.