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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

An observer is using an astronomical refracting telescope to observe planets in normal adjustment. The focal lengths of the objective and eyepiece used in the telescope construction are 20 m20 \text{ m} and 2 cm2 \text{ cm} respectively. Consider the following statements about the telescope: (A) The distance between the objective and the eyepiece is 20.02 m20.02 \text{ m}. (B) The magnification of the telescope is −1000-1000. (C) The image of the planet is erect and diminished. (D) The aperture of the eyepiece is smaller than that of the objective.

The correct statements are:

A

A, B, and C

B

B, C, and D

C

C, D, and A

D

A, B, and D

Step-by-Step Solution

  1. Analyze Given Data:
  • Focal length of objective (fof_o) = 20 m20 \text{ m}.
  • Focal length of eyepiece (fef_e) = 2 cm=0.02 m2 \text{ cm} = 0.02 \text{ m}.
  • Normal adjustment implies the final image is formed at infinity.
  1. Evaluate Statement A (Length):
  • In normal adjustment, the distance between the lenses (length of the telescope, LL) is the sum of their focal lengths.
  • L=fo+fe=20 m+0.02 m=20.02 mL = f_o + f_e = 20 \text{ m} + 0.02 \text{ m} = 20.02 \text{ m}.
  • Statement A is Correct.
  1. Evaluate Statement B (Magnification):
  • The magnifying power (mm) in normal adjustment is given by m=−fo/fem = -f_o / f_e.
  • m=−20/0.02=−1000m = -20 / 0.02 = -1000.
  • The negative sign indicates the image is inverted.
  • Statement B is Correct.
  1. Evaluate Statement C (Image Nature):
  • An astronomical refracting telescope produces an inverted image. It is not erect.
  • Statement C is Incorrect.
  1. Evaluate Statement D (Aperture):
  • The objective lens must have a large aperture to gather sufficient light from distant objects and to provide high resolution (RP∝aRP \propto a). The eyepiece has a smaller aperture.
  • Statement D is Correct.
  1. Conclusion: Statements A, B, and D are correct.

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 INSTRUMENTSobserverastronomicalrefractingtelescopeobserve

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