Question

The size of an object by a convex lens of focal length 20 cm is observed to be reduced to 1/3rd of its size.Find the distance of the object from the optical centre of the lens.

Answer 1

answer : object distance from the optical centre of the lens is 80cm.
explanation : focal length of convex lens , f = +20cm
a/c to question,
size of image = 1/3 × size of object.
so, magnification , m = -1/3
we know, magnification of lens , m = v/u
so, v/u = -1/3
so, v = -u/3 ........(1)
now applying lens maker formula,
1/v - 1/u = 1/f
or, 1/(-u/3) - 1/u = 1/20
or, -3/u - 1/u = 1/20
or, u = -80 cm
hence, object is placed 80cm from the pole of convex lens.

Answer 2

hi mate,

Solution: object distance from the optical centre of the lens is 80cm.

explanation : focal length of convex lens , f = +20cm

a/c to question,

size of image = 1/3 × size of object.

so, magnification , m = -1/3

we know, magnification of lens , m = v/u

so, v/u = -1/3

so, v = -u/3 ........(1)

now applying lens maker formula,

1/v - 1/u = 1/f

or, 1/(-u/3) - 1/u = 1/20

or, -3/u - 1/u = 1/20

or, u = -80 cm

hence, object is placed 80cm from the pole of convex lens.

i hope it helps you.