Under which of the following conditions a concave mirror can form a real image larger than the actual object ?

Options

A. When the object is kept at a distance equal to its radius of curvature
B. When object is kept at a distance less than its focal length
C. When object is placed between the focus and centre of curvature
D. When object is kept at a distance greater than its radius of curvature

Explanation

To determine the conditions under which a concave mirror can form a real image larger than the actual object, we need to analyze the properties of concave mirrors and the relationship between object distance, image distance, and magnification.

### Step-by-Step Solution:

1. **Understanding Image Formation by Concave Mirrors**:
- A concave mirror can form both real and virtual images depending on the position of the object relative to the mirror's focal point (F) and center of curvature (C).

2. **Magnification Concept**:
- The magnification (m) produced by a mirror is given by the formula:
\[ m = \frac{h'}{h} = -\frac{v}{u} \]
where \( h' \) is the height of the image, \( h \) is the height of the object, \( v \) is the image distance, and \( u \) is the object distance.
- For a real image to be larger than the object, the magnification must be greater than 1 (i.e., \( |m| > 1 \)).

3. **Analyzing the Given Options**:
- **Option 1**: When the object is at a distance equal to its radius of curvature (2F).
- At this position, the image formed is of the same size as the object (magnification = 1). Thus, this option does not satisfy our condition.

- **Option 2**: When the object is kept at a distance less than its focal length (F).
- In this case, the image formed is virtual and upright, which does not meet our requirement for a real image. Therefore, this option is also incorrect.

- **Option 3**: When the object is placed between the focus (F) and the center of curvature (C).
- Here, the image formed is real and inverted, and it is larger than the object. This is the correct condition for forming a real image larger than the object.

- **Option 4**: When the object is kept at a distance greater than its radius of curvature (2F).
- In this scenario, the image formed is real but smaller than the object (diminished). Hence, this option does not satisfy the condition.

4. **Conclusion**:
- The only condition under which a concave mirror can form a real image larger than the actual object is when the object is placed between the focus (F) and the center of curvature (C).

### Final Answer:
**The correct condition is when the object is placed between the focus and the center of curvature of the concave mirror.**