When an object lies at the focus of a concave mirror, them the position of the image formed and its magnification are

Options

A. pole and unity
B. infinity and unity
C. infinity and infinty
D. centre of curvature and unity

Answer

To solve the question regarding the position of the image formed and its magnification when an object lies at the focus of a concave mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- A concave mirror has a focus (F) and a center of curvature (C). The object is placed at the focus (F) of the concave mirror.

2. **Ray Diagram Analysis**:
- When an object is placed at the focus of a concave mirror, the rays of light emanating from the object will travel parallel to the principal axis after reflecting off the mirror.
- Since these rays are parallel, they will not converge to form a real image.

3. **Image Characteristics**:
- The rays reflected from the mirror will appear to diverge from a point behind the mirror. This means that the image formed will be virtual.
- The image will be erect (not inverted) and highly enlarged.

4. **Position of the Image**:
- The virtual image will be formed at the pole of the mirror (the vertex of the mirror), as the rays do not converge but appear to come from that point.

5. **Magnification Calculation**:
- The magnification (m) of a mirror is given by the formula:
\[ m = -\frac{v}{u} \]
where \(v\) is the image distance and \(u\) is the object distance.
- When the object is at the focus, the object distance \(u\) is equal to the focal length (F), and since the image is virtual, the image distance \(v\) will be equal to the distance from the pole to the virtual image, which can be considered as the same as the object distance in magnitude but opposite in sign.
- Thus, \(m = -\frac{(-u)}{u} = 1\).

6. **Conclusion**:
- Therefore, when an object is placed at the focus of a concave mirror, the position of the image formed is at the pole of the mirror, and the magnification is unity (1).

### Final Answer:
- **Position of the Image**: At the pole of the mirror.
- **Magnification**: Unity (1).