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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

A convex lens A of focal length 20 cm20\text{ cm} and a concave lens B of focal length 5 cm5\text{ cm} are kept along the same axis with the distance dd between them. If a parallel beam of light falling on A leaves B as a parallel beam, then distance dd in cm will be:

A

25

B

15

C

30

D

50

Step-by-Step Solution

  1. Analysis of Lens A (Convex): A parallel beam of light incident on a convex lens converges at its principal focus. Therefore, lens A attempts to form an image at a distance vA=fA=+20 cmv_A = f_A = +20\text{ cm} from its optical center.
  2. Analysis of Lens B (Concave): For the light rays emerging from lens B to be parallel, the object for lens B must be located at its focal point (or effectively, the rays entering B must be directed towards its focus on the other side).
  3. Afocal System Condition: When a combination of lenses receives parallel light and emits parallel light, the separation distance dd is the algebraic sum of their focal lengths: d=fA+fBd = f_A + f_B.
  4. Calculation: fA=+20 cmf_A = +20\text{ cm} (Convex) fB=−5 cmf_B = -5\text{ cm} (Concave)
  • d=20+(−5)=15 cmd = 20 + (-5) = 15\text{ cm}.
  1. Alternative Method (Lens Formula): The image formed by A acts as a virtual object for B. Let the distance be dd. Object distance for B: uB=+(20−d)u_B = +(20 - d) (since the rays are converging towards a point 20 cm20\text{ cm} from A). Final image distance for B: vB=∞v_B = \infty (parallel beam).
  • Using 1v−1u=1f\frac{1}{v} - \frac{1}{u} = \frac{1}{f} for lens B: 1∞−120−d=1−5\frac{1}{\infty} - \frac{1}{20 - d} = \frac{1}{-5} 0−120−d=−150 - \frac{1}{20 - d} = -\frac{1}{5} 120−d=15\frac{1}{20 - d} = \frac{1}{5} 20−d=5  ⟹  d=15 cm20 - d = 5 \implies d = 15\text{ cm}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from RAY OPTICS AND OPTICAL INSTRUMENTS. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSconvexlengthconcavelengthdistance

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