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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSMedium

Question

The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. The refractive index of the material of the lens is:

A

4/3

B

9/8

C

5/3

D

3/2

Step-by-Step Solution

  1. Identify Given Data:
  • Power of the lens, P=+10 DP = +10 \text{ D} (converging lens).
  • Radius of curvature, R=10 cm=0.1 mR = 10 \text{ cm} = 0.1 \text{ m}.
  • For a biconvex lens, using the sign convention: R1=+RR_1 = +R and R2=−RR_2 = -R.
  1. Lens Maker's Formula: The power of a lens is given by: P=(μ−1)(1R1−1R2)P = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)
  2. Calculation: Substituting the values into the formula: 10=(μ−1)(10.1−1−0.1)10 = (\mu - 1) \left( \frac{1}{0.1} - \frac{1}{-0.1} \right) 10=(μ−1)(10.1+10.1)10 = (\mu - 1) \left( \frac{1}{0.1} + \frac{1}{0.1} \right) 10=(μ−1)(20.1)10 = (\mu - 1) \left( \frac{2}{0.1} \right) 10=(μ−1)(20)10 = (\mu - 1) (20) μ−1=1020=0.5\mu - 1 = \frac{10}{20} = 0.5 μ=1+0.5=1.5=32\mu = 1 + 0.5 = 1.5 = \frac{3}{2}
  3. Conclusion: The refractive index of the material is 1.5 or 3/2.

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 INSTRUMENTSbiconvexdioptreradiuscurvaturesurface

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