An object is moving towards a converging lens on its axis. The image is also found to be moving towards the lens. Then, the object distance u must satisfy

Options

A. `2f lt u lt 4f`
B. `f lt u lt 2f`
C. `u gt 4f`
D. `u lt f`

Explanation

To solve the problem, we need to analyze the behavior of a converging lens when an object is moving towards it, and how this affects the image formation.

### Step-by-Step Solution:

1. **Understanding the Lens System**:
- We have a converging lens, which has a focal point (F) and a pole (P). The distance from the pole to the focus is called the focal length (f).

2. **Object Movement**:
- The object is moving towards the lens along its axis. As the object approaches the lens, we need to determine how the image behaves.

3. **Image Formation**:
- According to the lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where \( v \) is the image distance and \( u \) is the object distance. For a converging lens, both \( u \) and \( v \) are negative when measured from the lens.

4. **Condition for Image Movement**:
- The problem states that as the object moves towards the lens, the image also moves towards the lens. This implies that the image distance \( v \) must be decreasing (becoming less negative).

5. **Position of the Object**:
- If the object is placed at the focal point (F), the image is formed at infinity. As the object moves from the focal point towards the lens (P), the image moves from infinity towards the lens.
- Therefore, when the object is between the focus (F) and the pole (P), the image will be formed between the focus and the lens.

6. **Conclusion**:
- For the image to move towards the lens as the object moves towards it, the object distance \( u \) must be less than the focal length \( f \). Thus, we conclude:
\[ u < f \]

### Final Answer:
The object distance \( u \) must satisfy \( u < f \).

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