If we say that the focal length of a spherical mirror is n times its radius of curvature, then n must be

Options

A. `2.0`
B. `1.5`
C. `0.2`
D. none of these

Explanation

To solve the question, we need to understand the relationship between the focal length (f) and the radius of curvature (R) of a spherical mirror. The formula that relates these two quantities is:

1. **Understanding the Relationship**: The focal length (f) of a spherical mirror is given by the formula:
\[ f = \frac{R}{2} \]
where R is the radius of curvature.

2. **Expressing in Terms of n**: The question states that the focal length is n times the radius of curvature. We can express this as:
\[ f = n \cdot R \]

3. **Setting the Equations Equal**: Since we have two expressions for f, we can set them equal to each other:
\[ n \cdot R = \frac{R}{2} \]

4. **Solving for n**: To find n, we can divide both sides of the equation by R (assuming R is not zero):
\[ n = \frac{1}{2} \]

5. **Conclusion**: Therefore, the value of n must be:
\[ n = 0.5 \]

6. **Final Answer**: Since the options given do not include 0.5, the correct answer would be "None of these".