A concave mirror has a local length of 2m in vacuum. What would be its focal length when used in a medium of refractive index `2.759` ?

Options

A. `2m`
B. `2xx2.759m`
C. `2//2.759m`
D. Data inadequatc

Answer

To solve the problem, we need to understand the behavior of a concave mirror and how its focal length is affected by the medium in which it is placed.

### Step-by-Step Solution:

1. **Identify the Focal Length in Vacuum**:
The focal length of the concave mirror in vacuum is given as \( f = 2 \, \text{m} \).

2. **Understand the Concept of Focal Length**:
The focal length of a concave mirror is a property that depends on the shape of the mirror and not on the medium in which it is placed.

3. **Consider the Effect of the Medium**:
The refractive index of the medium is given as \( n = 2.759 \). However, for mirrors, the focal length does not change when placed in different media because the process involved is reflection, not refraction.

4. **Conclusion**:
Since the focal length is determined by the mirror's geometry and is independent of the medium, the focal length of the concave mirror remains the same even when placed in a medium with a refractive index of \( 2.759 \). Therefore, the focal length in the medium is still \( f = 2 \, \text{m} \).

### Final Answer:
The focal length of the concave mirror when used in a medium of refractive index \( 2.759 \) is \( 2 \, \text{m} \).

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