Question

The size of an object by a convex lens of focal length 20cm 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

We have,

Focal length=20 cm.

Let the height of object be h cm and height of image be h' cm.

Now ,by condition,

h'=h/3

But since it is a convex lens, the image is real and inverted.

Then, h' = - h/3 cm ....(1)

Now, m=h'/h

m=(-h/3)/h

V/u= -1/3 => v=-u/3.

By lens formula,

1/f = 1/v - 1/u

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

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

1/20=-4/u

u= -80 cm.

Hence the distance of object from the lens is 80cm.