Question

the size of image of an object by a convex lens of focal length 20cm is observed to be reduced to 1/3 of its size . find the distance of the object from optical center​

Answer 1

Answer:

The distance of the object is 80 cm.

Explanation:

Given that,

Focal length f = 20 cm

Magnification $m=\dfrac{1}{3}$

We know that,

The magnification is the ratio of the distance of the object and the distance of the image from the lens.

The magnification is

$-\dfrac{1}{3}=\dfrac{v}{u}$

$v = -\dfrac{1}{3}u$

The distance of the object is

Using lens formula

$\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$

$\dfrac{1}{20}=-\dfrac{3}{u}-\dfrac{1}{u}$

$u = -80\ cm$

Hence, The distance of the object is 80 cm.

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.