Assertion : A concave mirror of focal length f in air is used in a medium of refractive index 2. Then the focal length of mirror in medium becomes double.
Reason: The radius of curvature of a mirror is double of the focal length.

Options

A. If both assertion and reason are true and\ reason is a correct explanation of the assertion
B. If both assertion and reason are true but the reason is not a correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true

Answer

To solve the problem, we need to analyze both the assertion and the reason provided in the question.

### Step 1: Analyze the Assertion
The assertion states that "A concave mirror of focal length f in air is used in a medium of refractive index 2. Then the focal length of the mirror in the medium becomes double."

- **Understanding Focal Length in Different Mediums**: The focal length of a concave mirror is independent of the refractive index of the medium. The focal length \( f \) of a concave mirror remains the same regardless of the surrounding medium. Therefore, when the mirror is placed in a medium with a refractive index of 2, its focal length does not change.

**Conclusion for Assertion**: The assertion is **false**.

### Step 2: Analyze the Reason
The reason states that "The radius of curvature of a mirror is double the focal length."

- **Understanding the Relationship**: The relationship between the focal length \( f \) and the radius of curvature \( R \) of a mirror is given by the formula:
\[ f = \frac{R}{2} \]
This means that the radius of curvature is actually double the focal length, as \( R = 2f \).

**Conclusion for Reason**: The reason is **true**.

### Final Conclusion
- The assertion is false, and the reason is true. Therefore, the correct option is that the assertion is false and the reason is true.

### Summary of Steps
1. **Analyze the assertion**: Focal length remains the same in different mediums.
2. **Analyze the reason**: The relationship between focal length and radius of curvature is correctly described.
3. **Conclude**: Assertion is false, reason is true.