Question

A point object O is placed at a distance of $0.3\text{m}$ from a convex lens (focal length $0.2\text{m}$) cut into two halves each of which is displaced by $0.0005\text{m}$ as shown in the figure.



Find the spacing between the images so formed.

• A. $0.1cm$
• B. $0.5cm$
• C. $0.3cm$
• D. $1cm$

Answer 1

The correct option is C $0.3cm$

Each half lens is capable of producing a complete image and the focal length and nature of the lenses is same as the original lens. Only intensity of the image produced by each is decreased

For the two lenses, the principal axes are shifted as shown in the figure. Now, the point object will behave like an extended object with respect to both the half lenses.

For the top half and bottom half lens, two separate images will be formed.


Using the lens formula for the top half,

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

$\frac{1}{20}=\frac{1}{v}-\frac{-1}{30}$

$v=60cm$

If $h$ is the distance of the new principal axis of the upper lens from the original principal axis, then apparent height of the extended object is also $h$. If $h^{\prime }$ is the apparent height of the extended image formed by the upper half-lens,

$\frac{h^{\prime }}{h}=m=\frac{v}{u}=\frac{60}{-30}=-2$

$\Rightarrow h^{\prime }=2\times 0.05cm=0.1cm$

Distance between the two point images can be found by summing the apparent distance of each point image from the principal axis and the separation between the two principal axes.

Hence, separation between the two point images $=2h^{\prime }+2h=2\times 0.1+2\times 0.05=0.3cm$