A lens behaves as a converging lens in air and as a diverging lens in water. If refractive index of water is `1.33`, the refractive index of the material of the lens will be

Options

A. Equal to unity
B. Equal to 1.33
C. Between unity and 1.33
D. Greater than 1.33

Answer

To solve the problem, we need to analyze the behavior of the lens in two different mediums: air and water.

### Step-by-Step Solution:

1. **Understanding the Lens Behavior**:
- The lens behaves as a converging lens in air and a diverging lens in water.
- This means that in air, the refractive index of the lens material (let's denote it as \( n \)) must be greater than the refractive index of air (which is approximately 1).

2. **Refractive Index in Air**:
- Since the lens is converging in air, we have:
\[ n > 1 \]

3. **Refractive Index in Water**:
- The refractive index of water is given as \( n_{water} = 1.33 \).
- The lens behaves as a diverging lens in water, which implies that the refractive index of the lens material must be less than that of water:
\[ n < 1.33 \]

4. **Combining the Inequalities**:
- From the above two points, we can combine the inequalities:
\[ 1 < n < 1.33 \]
- This means the refractive index of the lens material is greater than 1 but less than 1.33.

5. **Conclusion**:
- The refractive index of the material of the lens must satisfy the condition \( 1 < n < 1.33 \).

### Final Answer:
The refractive index of the material of the lens is between 1 and 1.33.

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