Question

On a page turned sideways draw a horizontal line to represent the axis. Near the middle of this line, draw a 3 cm arrow to represent an image created by some lens not yet drawn. At a distance 2 cm to the right of this image, draw a 2 cm arrow to represent the object that produced this image (Both arrows should point up).

1. Use ray 2 to figure out the only place the lens can be placed to produce the image

Answer 1

In the figure u = object distance ,        h1= size of object AB

v = image distance = ( u+2 ) c.m (from fig)                    h2 = size of image A'B'

since image form is virtual , erect and magnified so the lens will be convex lens.

In convex lens , for virtual image :

linear magnification m = h2 / h1 = v / u

3 / 2 = u+2 / u

3u = 2u + 4

u= 4 c.m    ( hence lens should be placed 4 cm away from the object to produce the image of 3 cm height)

( also v = u+2 = 6 cm,

h2/h1 = v/u

h2 = (v/u)* h1

= (6/4) * 2

h2 = 3cm                ( ie if we are placing the lens at a distance 4 cm away from the object, image height comest out 3 cm which is same as given in the question)