Question: 11. A convex lens ‘A’ of focal length 20 cm and a concave lens ‘ B ‘ of focal length 5 cm are kept along the same axis with a distance ‘ d ‘ between them. If a parallel beam of light falling on ‘A’ leaves ‘ B ‘ as a parallel beam, then the distance ‘d’ in cm will be :
(1) 25
(2) 15
(3) 50
(4) 30
Answer: Option (2)
Explanation:
When a parallel beam of light falls on a convex lens, it converges at the principal focus of the lens.
The focal length of convex lens A is f_1 = 20\,\text{cm},
so the image formed by lens A will be at a distance of 20\,\text{cm} from it.
For a concave lens to produce parallel rays as output,
the object for the lens must be placed at its principal focus.
The focal length of concave lens B is f_2 = -5\,\text{cm}.
Hence, the object must be located 5\,\text{cm} to the right of lens B.
Let the distance between the two lenses be d.
The image formed by lens A is at 20\,\text{cm} from A,
which acts as the object for lens B.
So, the distance of this object from lens B is 20 - d.
For the rays to emerge parallel from lens B,
this distance must be equal to 5\,\text{cm}.
Thus, 20 - d = 5.
Solving, d = 15\,\text{cm}.
Therefore, the correct answer is Option (2).