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NEET PHYSICSRAY OPTICS AND OPTICAL INSTRUMENTSEasy

Question

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index:

A

equal to that of glass

B

less than one

C

greater than that of glass

D

less than that of glass

Step-by-Step Solution

  1. Lens Maker's Formula: The focal length (ff) of a lens is given by the formula: 1f=(μgμl−1)(1R1−1R2)\frac{1}{f} = \left( \frac{\mu_g}{\mu_l} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) where μg\mu_g is the refractive index of the lens material (glass) and μl\mu_l is the refractive index of the surrounding medium (liquid).
  2. Condition for Plane Sheet: A plane sheet of glass has an infinite focal length (f=∞f = \infty) because it does not converge or diverge light (Power P=1f=0P = \frac{1}{f} = 0).
  3. Application: For 1f\frac{1}{f} to be zero, the term (μgμl−1)\left( \frac{\mu_g}{\mu_l} - 1 \right) must be zero (assuming radii of curvature R1,R2R_1, R_2 are finite). μgμl−1=0  ⟹  μgμl=1  ⟹  μg=μl\frac{\mu_g}{\mu_l} - 1 = 0 \implies \frac{\mu_g}{\mu_l} = 1 \implies \mu_g = \mu_l.
  4. Conclusion: For the lens to lose its optical power and behave like a plane sheet, the refractive index of the liquid must be equal to the refractive index of the glass (1.47).

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 INSTRUMENTSbiconvexhavingrefractivedippedliquid

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