An object is placed at the centre of curvature C of a concave mirror, the image formed will be at

Options

A. Focus
B. Infinity
C. Between C and F
D. Centre of curvature C.

Explanation

To determine where the image is formed when an object is placed at the center of curvature (C) of a concave mirror, we can follow these steps:

### Step 1: Understand the Position of the Object
- The object is placed at the center of curvature (C) of the concave mirror. The center of curvature is located at a distance equal to the radius of curvature (R) from the mirror's surface.

### Step 2: Use the Mirror Formula
- The mirror formula relates the object distance (u), image distance (v), and focal length (f) of the mirror:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
- For a concave mirror, the focal length (f) is negative, and the object distance (u) is also negative (since the object is in front of the mirror).

### Step 3: Identify Distances
- The distance of the object from the mirror (u) when it is at the center of curvature is:
\[ u = -R \]
- The focal length (f) of a concave mirror is:
\[ f = -\frac{R}{2} \]

### Step 4: Substitute Values into the Mirror Formula
- Substitute \(u = -R\) and \(f = -\frac{R}{2}\) into the mirror formula:
\[ \frac{1}{-\frac{R}{2}} = \frac{1}{v} + \frac{1}{-R} \]
- This simplifies to:
\[ -\frac{2}{R} = \frac{1}{v} - \frac{1}{R} \]

### Step 5: Solve for Image Distance (v)
- Rearranging gives:
\[ \frac{1}{v} = -\frac{2}{R} + \frac{1}{R} = -\frac{1}{R} \]
- Therefore:
\[ v = -R \]

### Step 6: Conclusion
- The image distance (v) is also at the center of curvature (C), but since it is negative, it indicates that the image is formed on the same side as the object.
- Thus, the image formed is at the center of curvature (C).

### Final Answer
The image formed will be at the center of curvature (C).

---