The focal length (f) of a spherical mirror of radius of curvature R is

Options

A. R
B. `R/2`
C. `(3R)/2`
D. 2R

Answer

To find the focal length (f) of a spherical mirror given its radius of curvature (R), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The **radius of curvature (R)** is the distance from the mirror's surface to its center of curvature.
- The **focal length (f)** is the distance from the mirror to its focal point, where parallel rays of light either converge (in concave mirrors) or appear to diverge from (in convex mirrors).

2. **Identify the Relationship**:
- The relationship between the focal length and the radius of curvature for spherical mirrors is given by the formula:
\[ f = \frac{R}{2} \]
- This formula holds true for both concave and convex mirrors.

3. **Apply the Formula**:
- If you have a spherical mirror and you know its radius of curvature (R), you can simply substitute R into the formula to find the focal length (f).
- For example, if \( R = 10 \, \text{cm} \), then:
\[ f = \frac{10 \, \text{cm}}{2} = 5 \, \text{cm} \]

4. **Conclusion**:
- The focal length of a spherical mirror is always half of its radius of curvature. Therefore, regardless of whether the mirror is concave or convex, the focal length can be calculated using the same formula.

### Final Answer:
The focal length (f) of a spherical mirror of radius of curvature (R) is given by:
\[ f = \frac{R}{2} \]