Question

A point object O is placed at distance of 0.3 m from a convex lens (focal length = 0.2 m) cut into two halves each of which is displaced by 0.0005 m as shown.
What will be the location of the image?

A) 30 cm, right of lens
B) 60 cm, right of lens
C) 70 cm, left of lens
D) 40 cm, left of lens

Answer 1

Hint: After the cutting of the lens into two halves, the focal length will remain the same. Use the lens formula to find the image distance.

Complete step by step answer:
When a symmetric lens is cut along the principal axis in two equal parts, the focal length will remain same and intensity of image formed by each part will be less as compared with the complete lens. whereas when as symmetric lens is cut along the optical axis into two parts, the focal length becomes double of the original and intensity will be same as that of the complete lens.
According to question it is given that
Distance of object $ = 0.3m = 30cm$
Focal length of lens $ = 0.2m = 20cm$
Each half lens will form an image in the same plane. Then, by using the lens formula:
$
  \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} \\
   \Rightarrow \dfrac{1}{v} = \dfrac{1}{f} + \dfrac{1}{u} \\
 $

(where, $f = $focal length, $v = $distance of image and $u = $object distance
Putting the values in above equation
$
  \dfrac{1}{v} = \dfrac{1}{{20}} + \dfrac{1}{{\left( { - 30} \right)}} \\
   \Rightarrow \dfrac{1}{v} = \dfrac{{10}}{{600}} \\
   \Rightarrow v = 60cm \\
 $
So, the location of the image formed will be 60 cm since this is a positive value so it will form at the right side of the lens.
Therefore, the correct option is (B).

Note: During the construction of ray diagram, keep in mind that convex lens converges incident rays to the principal axis and it is thick at center and thin at edges.