When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of

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:

Accepted Answer

1.  **Lens Maker's Formula:** The focal length ($f$) of a lens is given by the formula:
    $\frac{1}{f} = \left( \frac{\mu_g}{\mu_l} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$
    where $\mu_g$ is the refractive index of the lens material (glass) and $\mu_l$ is the refractive index of the surrounding medium (liquid).
2.  **Condition for Plane Sheet:** A plane sheet of glass has an infinite focal length ($f = \infty$) because it does not converge or diverge light (Power $P = \frac{1}{f} = 0$).
3.  **Application:** For $\frac{1}{f}$ to be zero, the term $\left( \frac{\mu_g}{\mu_l} - 1 \right)$ must be zero (assuming radii of curvature $R_1, R_2$ are finite).
    $\frac{\mu_g}{\mu_l} - 1 = 0 \implies \frac{\mu_g}{\mu_l} = 1 \implies \mu_g = \mu_l$.
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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