The distance between the principal focus and centre of curvature of the convex mirror is equal to ___

Options

A. 3f
B. R/2
C. f/2
D. 2R

Explanation

To solve the question regarding the distance between the principal focus (F) and the center of curvature (C) of a convex mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The **principal focus (F)** of a convex mirror is the point where parallel rays of light either converge or appear to diverge from after reflecting off the mirror.
- The **center of curvature (C)** is the center of the sphere from which the mirror is a part.

2. **Identify the Distances**:
- The distance from the pole (P) of the mirror to the center of curvature (C) is denoted as \( R \) (radius of curvature).
- The distance from the pole (P) to the principal focus (F) is denoted as \( f \) (focal length).

3. **Establish the Relationship**:
- For a convex mirror, the relationship between the focal length and the radius of curvature is given by:
\[ R = 2f \]
- This means that the radius of curvature \( R \) is twice the focal length \( f \).

4. **Calculate the Distance Between F and C**:
- The distance between the principal focus (F) and the center of curvature (C) can be expressed as:
\[ FC = PC - PF \]
- Since \( PC = R \) and \( PF = f \), we can substitute:
\[ FC = R - f \]

5. **Substituting the Relationship**:
- We know from the relationship \( R = 2f \), so we can substitute \( R \) in the equation:
\[ FC = 2f - f \]
- Simplifying this gives:
\[ FC = f \]

6. **Final Expression**:
- Therefore, the distance between the principal focus (F) and the center of curvature (C) of the convex mirror is equal to:
\[ FC = \frac{R}{2} \]

### Conclusion:
The distance between the principal focus and the center of curvature of the convex mirror is equal to \( \frac{R}{2} \).