The graph between `u` and `v` for a convex mirrorr is

Options

A.
B.
C.
D.

Explanation

To determine the graph between `u` (object distance) and `v` (image distance) for a convex mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Convex Mirrors**:
- Convex mirrors always produce virtual, upright, and diminished images. The image distance `v` is always negative for a convex mirror, as per the sign convention.

2. **Ray Diagram Analysis**:
- When the object is placed at a very large distance (u → ∞), the rays coming from the object are parallel. These rays appear to diverge from the focus behind the mirror. Therefore, the image is formed at the focus (v = -f).
- As the object comes closer to the mirror (decreasing `u`), the image distance `v` also changes. The image moves closer to the mirror as `u` decreases.

3. **Behavior of `u` and `v`**:
- As `u` approaches infinity (very far away), `v` approaches the focus (which is a negative value).
- As `u` decreases and approaches the mirror, `v` will also decrease (becoming less negative) but will always remain negative.

4. **Graph Characteristics**:
- The graph between `u` and `v` will show that as `u` increases (moving towards infinity), `v` approaches a constant negative value (the focus).
- As `u` decreases (moving towards the mirror), `v` will also decrease but will remain negative, indicating that the image is moving closer to the mirror.

5. **Conclusion**:
- The correct graph will show a curve that approaches the x-axis (u-axis) as `u` increases and will also approach the y-axis (v-axis) as `u` decreases, indicating that `v` is negative and approaches zero but never becomes positive.

### Final Result:
The graph between `u` and `v` for a convex mirror is a curve that approaches the x-axis as `u` increases and approaches the y-axis as `u` decreases, indicating the relationship between the object distance and the image distance.