A convergent lens of focal length 20cm and made of a material with refractive index 1.1 is immersed in water. The lens will behave as a

Options

A. Converging lens of focal length 20cm
B. Converging lens of focal length less than 20cm
C. Converging lens of focal length more than 20cm
D. Divergent lens

Answer

To solve the problem, we need to determine how a convergent lens behaves when it is immersed in water, given its focal length and refractive index. We will use the Lensmaker's formula and the concept of refractive indices.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Focal length of the lens in air, \( f = 20 \, \text{cm} \)
- Refractive index of the lens material, \( \mu_L = 1.1 \)
- Refractive index of water, \( \mu_W = \frac{4}{3} \approx 1.33 \)

2. **Determine the Refractive Index of the Lens with Respect to Water:**
- The refractive index of the lens with respect to water can be calculated using the formula:
\[ \mu_{LW} = \frac{\mu_L}{\mu_W} \]
- Substituting the values:
\[ \mu_{LW} = \frac{1.1}{1.33} \approx 0.826 \]

3. **Analyze the Result:**
- Since \( \mu_{LW} < 1 \), this indicates that the lens behaves as a divergent lens when immersed in water.

4. **Conclusion:**
- The lens, originally a convergent lens in air, will now act as a divergent lens when placed in water due to the fact that the refractive index of the lens material is less than that of the surrounding medium (water).

### Final Answer:
The lens will behave as a **divergent lens** when immersed in water.

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