Question

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

What will be the location of the image?

• A. $30cm,$ right of lens
• B. $60cm,$ right of lens
• C. $70cm,$ left of lens
• D. $40cm,$ left of lens

Answer 1

The correct option is B $60cm,$ right of lens

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,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{20}=\frac{1}{v}-\frac{-1}{30}$
$v=60cm$

So the image will be formed $60cm$ right of the lens.