Question

Assertion (A) : When a convex lens made of glass is immersed in water, its converging power increases.
Reason (R) : The focal length of a lens depends only on the radii of curvature of its two faces.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

Whenever a lens is placed in a medium denser than air (but less dense than the lens material), the relative refractive index decreases, the focal length increases, and its optical power always decreases.\

Answer 1

The Correct Option is D

Concept:
• According to the Lens Maker's Formula, the focal length $f$ of a thin spherical lens is given by $\frac{1}{f} = \left(\frac{\mu_{\text{lens}}}{\mu_{\text{medium}}} - 1\right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)$.
• The converging power of a lens is inversely proportional to its focal length, expressed as $P = \frac{1}{f}$.
• The relative refractive index depends on both the material of the lens and the surrounding medium.

Step 1: Analyze the Assertion (A)
When a convex lens made of glass ($\mu_g \approx 1.5$) is placed in air ($\mu_a = 1$), the relative refractive index is $\frac{\mu_g}{\mu_a} = 1.5$.
When the same lens is immersed in water ($\mu_w \approx 1.33$), the relative refractive index becomes:
\[ \mu_{\text{rel}} = \frac{\mu_g}{\mu_w} = \frac{1.5}{1.33} \approx 1.125 \]
Since $\mu_{\text{rel}} - 1$ decreases significantly in water, the term $\frac{1}{f}$ decreases, which means the focal length $f$ increases ($f_w \approx 4 f_a$).
Since optical power $P = \frac{1}{f}$, the converging power of the lens decreases when immersed in water.
Therefore, Assertion (A) is false.

Step 2: Analyze the Reason (R)
From the Lens Maker's formula, the focal length of a lens depends on:
1. The refractive index of the material of the lens ($\mu_{\text{lens}}$).
2. The refractive index of the surrounding medium ($\mu_{\text{medium}}$).
3. The radii of curvature of its refracting faces ($R_1$ and $R_2$).
4. The wavelength/color of incident light.
Thus, focal length does not depend only on the radii of curvature of the faces.
Therefore, Reason (R) is false.

Step 3: Conclusion
Since both Assertion (A) and Reason (R) are false statements, option (D) is the correct choice.