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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).
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