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

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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 the Convex Mirror**:
- A convex mirror always forms a virtual image. The image is upright and diminished, regardless of the position of the object.

2. **Sign Convention**:
- For a convex mirror, the object distance `u` is taken as negative (since the object is on the same side as the incoming light).
- The image distance `v` is positive (since the image is formed on the opposite side of the mirror).

3. **Behavior at Infinity**:
- When the object is at a very large distance (approaching negative infinity, `u = -∞`), the rays coming from the object are parallel.
- These rays appear to diverge from the focus of the convex mirror, which is located behind the mirror. Thus, for `u = -∞`, the image distance `v` approaches the focal point `f` (which is a positive value).

4. **Closer Object Position**:
- As the object moves closer to the mirror (i.e., `u` increases towards 0 from negative values), the image distance `v` also increases.
- When the object is at the pole of the mirror (i.e., `u = 0`), the image distance `v` also approaches 0.

5. **Plotting the Graph**:
- On the graph, the x-axis represents `u` (object distance) and the y-axis represents `v` (image distance).
- The graph starts from the point where `u` is at `-∞` and `v` is at `f`, moving towards the point where `u` is 0 and `v` is also 0.
- The relationship is such that as `u` increases (becomes less negative), `v` also increases, showing a positive correlation.

6. **Conclusion**:
- The graph between `u` and `v` for a convex mirror will be a curve that starts from the point `(−∞, f)` and approaches the origin `(0, 0)`. This indicates that as the object distance increases (becomes less negative), the image distance also increases.