If the radius of curvature of a convex mirror is 4.00 m. What will be the focal length of the mirror?

Options

A. `+4 m `
B. `-4 m `
C. `+2 m `
D. ` -2 m `

Answer

To find the focal length of a convex mirror given its radius of curvature, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the Radius of Curvature (R)**:
The radius of curvature of the convex mirror is given as 4.00 m. Since we are dealing with a convex mirror, we consider the radius of curvature to be positive.
\[ R = +4.00 \, \text{m} \]

2. **Use the Formula for Focal Length (f)**:
The relationship between the focal length (f) and the radius of curvature (R) for mirrors is given by the formula:
\[ f = \frac{R}{2} \]

3. **Substitute the Value of R into the Formula**:
Now, substitute the value of R into the formula to find the focal length.
\[ f = \frac{4.00 \, \text{m}}{2} \]

4. **Calculate the Focal Length**:
Performing the division:
\[ f = 2.00 \, \text{m} \]

5. **Determine the Sign of the Focal Length**:
For a convex mirror, the focal length is also considered positive. Therefore, we conclude:
\[ f = +2.00 \, \text{m} \]

### Final Answer:
The focal length of the convex mirror is **+2.00 m**.

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