At what position does an object needs to be placed so that a concave mirror gives an image which is virtual in nature, erect and magnified as compared to the object?:

Options

A. at infinity
B. between P and F
C. beyond C
D. between C and F

Answer

To determine the position at which an object needs to be placed in front of a concave mirror to produce a virtual, erect, and magnified image, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of Concave Mirrors**:
- Concave mirrors can produce 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).
- A virtual image is formed when the object is placed between the focal point and the mirror.

2. **Identify the Requirements for the Image**:
- The image must be virtual, which means it cannot be projected on a screen.
- The image must be erect, meaning it has the same orientation as the object.
- The image must be magnified, indicating that it is larger than the object.

3. **Determine the Position of the Object**:
- For a concave mirror to produce a virtual, erect, and magnified image, the object must be placed between the mirror's focal point (F) and the mirror's pole (P).
- This specific position allows the light rays to diverge after reflecting off the mirror, making it appear as though they are coming from a point behind the mirror.

4. **Visualize the Ray Diagram**:
- Draw a ray diagram to illustrate this situation:
- Draw the principal axis, the mirror, the focal point (F), and the center of curvature (C).
- Place the object between P and F.
- Draw one ray parallel to the principal axis that reflects through the focal point.
- Draw another ray that goes through the center of curvature and reflects back on itself.
- Extend these rays backward to show where they appear to converge, indicating the position of the virtual image.

5. **Conclusion**:
- The object must be placed between the pole (P) and the focal point (F) of the concave mirror to achieve a virtual, erect, and magnified image.