As an object moves towards a convex mirror, the image

Options

A. magnification increases
B. moves towards the mirror
C. Neither (a) nor (b) happens
D. Both (1) and (2) happen

Answer

To solve the question "As an object moves towards a convex mirror, the image is...", we can analyze the behavior of images formed by convex mirrors using the mirror formula and the magnification concept.

### Step-by-Step Solution:

1. **Understanding the Properties of Convex Mirrors**:
- Convex mirrors always produce virtual, upright, and diminished images regardless of the position of the object.

2. **Using the Mirror Formula**:
- The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
- Here, \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance. For a convex mirror, the focal length \(f\) is positive, and the object distance \(u\) is negative (since the object is in front of the mirror).

3. **Analyzing the Movement of the Object**:
- As the object moves closer to the convex mirror, the absolute value of \(u\) (which is negative) decreases. This means that \(u\) becomes less negative (i.e., approaches zero).

4. **Effect on Image Distance \(v\)**:
- As \(u\) decreases, we can analyze how \(v\) behaves using the mirror formula. Since \(f\) is constant, a decrease in \(u\) will lead to an increase in \(v\) (the image distance). This means the image moves closer to the mirror.

5. **Magnification**:
- The magnification \(m\) is given by:
\[ m = -\frac{v}{u} \]
- As \(u\) decreases (becomes less negative), \(m\) increases in magnitude. This indicates that the image appears larger as the object approaches the mirror.

6. **Conclusion**:
- Therefore, as the object moves towards a convex mirror, the image moves towards the mirror and the magnification increases. Thus, both effects happen.

### Final Answer:
The correct option is **D: Both A and B happen**.