The distance of an object from a concave 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

Answer

To solve the problem, we need to analyze the situation where an object is placed at the focal point of a concave mirror. We can use the mirror formula to find the characteristics of the image formed.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The distance of the object (u) from the concave mirror is equal to the focal length (f) of the mirror.
- For a concave mirror, the focal length is considered negative, so we have:
\[ u = -f \]

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

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

4. **Simplify the Equation**:
- Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f} \]

5. **Find the Image Distance (v)**:
- Taking the reciprocal, we find:
\[ v = \frac{f}{2} \]
- However, since we are looking for the case when the object is at the focal point, we realize that the image distance approaches infinity as the object approaches the focal point.

6. **Conclusion**:
- When the object is placed at the focal point of a concave mirror, the rays of light reflecting off the mirror will be parallel, and thus the image is formed at infinity.

### Final Answer:
The image is formed at infinity.