Question

an image 2/3 of the size of the object is formed by a convex lens at a distance of 12cm from it. Find the focal length of the lens.

Answer 1

The image formed is real (convex lens forms diminished real image)

m= -2/3

v= + 12cm

m=v/u

-2/3=12/u

-2u=36

u= -18 cm

now

focal length formula

1/f= 1/v - 1/u

1/f= 1/12 - 1/(-18) = 5/36

f=36/5

focal length of the lens= 7.2cm

Answer 2

size of image = -2/3 × size of object.

or, magnification = size of image/ size of object = v/u

or, -2/3 × size of object/size of object = v/u

or, -2/3 = v/u

or, u = (3/2)v = -1.5v ..........(1)

image distance , v = 12cm

object distance , u = -1.5v = -1.5 × 12 = -18cm

use formula, 1/v - 1/u = 1/f

or, 1/12 - 1/-18 = 1/f

or, 1/12 + 1/18 = 1/f

or, 1/f = 5/36

hence, f = 7.2 cm