To solve the problem regarding the behavior of a converging beam of light incident on a concave mirror, we can follow these steps:
### Step 1: Understand the Basic Formula
The fundamental formula for a concave mirror is given by the mirror formula:
\[
\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
\]
where:
- \( f \) = focal length of the mirror
- \( v \) = image distance from the mirror
- \( u \) = object distance from the mirror
### Step 2: Identify the Nature of the Incident Beam
A converging beam of light means that the light rays are coming together at a point. When such a beam is incident on a concave mirror, we need to analyze the position of the object (where the converging rays are coming from) in relation to the focal point of the mirror.
### Step 3: Analyze Cases Based on Object Distance
We can categorize the position of the object based on its distance from the mirror relative to the focal length \( f \):
1. **Case 1: Object at Infinity (\( u \to \infty \))**
- When the object is at a very large distance, the rays are parallel to the principal axis.
- The reflected rays converge at the focal point, forming a real image at the focus.
- Here, \( v \) tends to \( f \).
2. **Case 2: Object Beyond the Focal Point (\( u > f \))**
- If the object is placed beyond the focal point, the rays will converge after reflection.
- The image formed will be real and inverted, located between the focal point and the center of curvature.
- In this case, \( v \) will be positive, indicating a real image.
3. **Case 3: Object at the Focal Point (\( u = f \))**
- If the object is placed at the focal point, the rays will reflect parallel to the principal axis.
- No image is formed at a finite distance; instead, the image is formed at infinity.
4. **Case 4: Object Between the Focal Point and the Mirror (\( u < f \))**
- If the object is located between the focal point and the mirror, the reflected rays diverge.
- The image formed will be virtual, upright, and located behind the mirror.
- Here, \( v \) will be negative, indicating a virtual image.
### Step 4: Conclusion
From the analysis, we can conclude:
- A converging beam of light incident on a concave mirror will always form a real image when the object is placed beyond the focal point.
- If the object is at the focal point, the image is formed at infinity.
- If the object is between the focal point and the mirror, a virtual image is formed.
Thus, the reflected light must form a real image when the object is beyond the focal point, and it can also form a virtual image when the object is between the focal point and the mirror.
### Final Answer
The reflected light from a concave mirror when a converging beam is incident can form:
1. A real image (when \( u > f \))
2. A virtual image (when \( u < f \))
