Which one of the following statements concerning a convex mirror is true?

Options

A. A convex mirror can form a real image.
B. A convex mirror must be spherical in shape.
C. The image produced by a convex mirror will always be inverted relative to the object.
D. The image a convex mirror produces is closer to the mirror than it would be in a plane mirror for the smae object distance.

Answer

To solve the question regarding which statement concerning a convex mirror is true, we will analyze each option systematically.

### Step-by-Step Solution:

1. **Understanding Convex Mirrors**:
- A convex mirror is a spherical mirror that bulges outward. It diverges light rays that strike its surface.

2. **Analyzing Option 1**:
- **Statement**: "A convex mirror can form a real image."
- **Explanation**: Convex mirrors always produce virtual images that are upright and smaller than the object. They do not form real images because the reflected rays diverge and do not converge to form a real image.
- **Conclusion**: This statement is **false**.

3. **Analyzing Option 2**:
- **Statement**: "Convex mirror must be spherical in shape."
- **Explanation**: While convex mirrors are derived from spherical surfaces, they are not strictly spherical in shape. They are typically small sections of a sphere, and the term "convex mirror" refers to the shape of the reflective surface, not the entire mirror.
- **Conclusion**: This statement is **false**.

4. **Analyzing Option 3**:
- **Statement**: "The image produced by a convex mirror always be inverted relative to the subject."
- **Explanation**: The image formed by a convex mirror is virtual, upright, and smaller than the object. The magnification (M) is positive, indicating that the image is upright.
- **Conclusion**: This statement is **false**.

5. **Analyzing Option 4**:
- **Statement**: "If the image of a convex mirror produces closer to the mirror, then it would be a plane mirror for small object distance."
- **Explanation**: When the object is placed very close to the convex mirror, the image appears behind the mirror at a distance that is approximately equal to the object distance. This behavior resembles that of a plane mirror, where the image distance equals the object distance.
- **Conclusion**: This statement is **true**.

### Final Answer:
The correct statement concerning a convex mirror is **Option 4**: "If the image of a convex mirror produces closer to the mirror, then it would be a plane mirror for small object distance."