The distance of an object from a spherical mirror is equal to the focal length of the mirror. Then the image:

Options

A. must be at infinity
B. may be at infinity
C. may be at the focus
D. none

Explanation

To solve the problem, we need to analyze the situation where the distance of an object from a spherical mirror is equal to the focal length of the mirror. We will consider both concave and convex mirrors to understand the behavior of the image formed under these conditions.

### Step-by-Step Solution:

1. **Identify the Type of Mirror**:
- We need to consider both concave and convex mirrors. For this solution, we will primarily focus on the concave mirror since it is the most common scenario when discussing focal lengths.

2. **Understand the Mirror Formula**:
- The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
where \( f \) is the focal length, \( v \) is the image distance, and \( u \) is the object distance.

3. **Set the Object Distance Equal to the Focal Length**:
- According to the problem, the object distance \( u \) is equal to the focal length \( f \). Therefore, we can write:
\[ u = f \]

4. **Substitute into the Mirror Formula**:
- Since \( u = f \), we can substitute this into the mirror formula:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{f} \]

5. **Simplify the Equation**:
- Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{f} - \frac{1}{f} = 0 \]
- This implies that:
\[ v \rightarrow \infty \]
- Therefore, the image is formed at infinity.

6. **Consider the Case of a Virtual Object**:
- If we consider a virtual object placed at the second focus of the concave mirror, the object distance would be negative. In this case, the image will not be at infinity but will be formed at a finite distance.

7. **Conclusion**:
- The image formed when the object distance equals the focal length can either be at infinity (for real objects) or at a finite distance (for virtual objects). Therefore, the correct answer to the question is that the image may be at infinity.

### Final Answer:
The image may be at infinity.