A converging lens of refractive index `1.5` is kept in a liquid medium having the same refractive index. What would be the focal length of the lens in the medium ?

Explanation

To find the focal length of a converging lens in a liquid medium with the same refractive index, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Refractive Indices**:
- The refractive index of the lens (\( \mu_1 \)) is given as 1.5.
- The refractive index of the medium (\( \mu_2 \)) is also given as 1.5.

2. **Use the Lens Maker's Formula**:
- The Lens Maker's Formula is given by:
\[ \frac{1}{f} = \left( \mu_2 - \mu_1 \right) \cdot \frac{1}{R_1} - \frac{1}{R_2} \]
- Where \( f \) is the focal length, \( R_1 \) is the radius of curvature of the first surface, and \( R_2 \) is the radius of curvature of the second surface.

3. **Substitute the Values**:
- Since \( \mu_1 = \mu_2 = 1.5 \):
\[ \frac{1}{f} = \left( 1.5 - 1.5 \right) \cdot \frac{1}{R_1} - \frac{1}{R_2} \]
- This simplifies to:
\[ \frac{1}{f} = 0 \cdot \frac{1}{R_1} - \frac{1}{R_2} \]
- Therefore:
\[ \frac{1}{f} = 0 \]

4. **Conclusion**:
- If \( \frac{1}{f} = 0 \), then:
\[ f = \infty \]
- This means that the focal length of the lens in the medium is infinite.

### Final Answer:
The focal length of the lens in the medium is infinity.

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