An inverted image can be seen in a convex mirror,

Options

A. under no circumstances
B. when the object is very far from the mirror
C. when the object is at a distance equal to the radius of curvature of the mirror
D. when the distance of the object from the mirror is equal to the focal length of the mirror

Explanation

### Step-by-Step Solution:

1. **Understanding Convex Mirrors**:
- A convex mirror is a type of mirror that curves outward. It always forms virtual images that are upright (erect) and smaller than the object.

2. **Analyzing the Image Formation**:
- In a convex mirror, the rays of light diverge after reflecting off the mirror. The extensions of these rays appear to converge behind the mirror, forming a virtual image.

3. **Considering Different Object Positions**:
- **Object at Infinity**: When the object is very far away (at infinity), the rays come in parallel and reflect off the mirror. They diverge, and the virtual image formed is upright.
- **Object at Center of Curvature**: If the object is placed at the center of curvature, the rays will reflect and still diverge, leading to a virtual image that is upright.
- **Object at Focal Point**: Similarly, if the object is at the focal point of the convex mirror, the rays will diverge again, resulting in a virtual and upright image.
- **Closer Object**: As the object moves closer to the mirror, the image remains virtual and upright.

4. **Conclusion**:
- Throughout all scenarios, the image formed by a convex mirror is never inverted. It is always virtual and erect. Therefore, the answer to the question is that an inverted image cannot be seen in a convex mirror under any circumstances.

### Final Answer:
An inverted image cannot be seen in a convex mirror under any circumstances.

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