Question

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

• A. 30
• B. 25
• C. 15
• D. 50

Answer 1

The Correct Option is C

To solve this problem, we need to understand the behavior of light as it passes through a combination of lenses. Here, we have a convex lens 'A' with a focal length \( f_A = +20 \, \text{cm} \) and a concave lens 'B' with a focal length \( f_B = -5 \, \text{cm} \). When a parallel beam of light passes through the convex lens and then the concave lens, it emerges as a parallel beam again. This happens when the lenses are separated by a particular distance 'd'.

Step-by-step reasoning: 

1. First, understand that the parallel beam of light converges at the focal point of the convex lens 'A'. Therefore, it focuses the light at its focal length, i.e., 20 cm from lens 'A'.
2. Next, for the light to emerge as a parallel beam after passing through the concave lens 'B', the light must appear to come from the focal point of lens 'B'. This would make the lens 'B' behave as if it does not diverge the light any further.
3. Since the lenses are along the same axis, for the beam to emerge parallel, the distance 'd' between the two lenses thus should equal the sum of the focal lengths of lens 'A' and the negative focal length of lens 'B', because the light converges at lens 'A' and diverges at lens 'B'.
4. The focal point of the concave lens is at the distance \( f_B = -5 \, \text{cm} \) from it. Consequently, the convex lens must place the light focus right at this distance.
5. Therefore, the condition for parallel beams after lens 'B' is: \(d = f_A + |f_B|\)

Calculating 'd':

• \(d = 20 \, \text{cm} + (-(-5 \, \text{cm}))\)
• \(d = 20 \, \text{cm} + 5 \, \text{cm} = 15 \, \text{cm}\)

From this calculation, we see that the required distance \( d \) for the light to emerge as a parallel beam after passing through both lenses is 15 cm.

Thus, the correct answer is 15 cm.