I is the image of a point object `O` formed by spherical mirror, then which of the following statements is incorrect :

Options

A. If `O` and `I` are on same side of the principal axis, the they have to be on opposite sides of the mirror.
B. If `O` and `I` are on opposite side of the principal axis, then they have to be on same side of the mirror.
C. If `O` and `I` are on opposite side of the principal axis, then they can be on opposite side of the mirror as well.
D. If `O` is on principal axis then `I` has to lie on principal axis only.

Explanation

To determine which statement is incorrect regarding the image formed by a spherical mirror, we can analyze the relationships between the object distance (u), image distance (v), and their respective heights (h_o for object height and h_i for image height) using the magnification formula.

### Step-by-Step Solution:

1. **Understanding the Magnification Formula**:
The magnification (m) is defined as:
\[ m = \frac{h_i}{h_o} = -\frac{v}{u} \]
Here, \(h_i\) is the height of the image, \(h_o\) is the height of the object, \(v\) is the image distance, and \(u\) is the object distance.

2. **Analyzing the Statements**:
We need to evaluate four statements regarding the positions of the object and image relative to the principal axis of the mirror.

3. **Statement 1**: If the object and image are on the same side of the principal axis (both above or both below).
- If both are above the principal axis, then \(h_o > 0\) and \(h_i > 0\).
- According to the sign convention, \(u\) is negative (object on the left) and \(v\) is also negative (image on the left).
- This statement is **correct**.

4. **Statement 2**: If the object and image are on opposite sides of the principal axis (object above and image below).
- Here, \(h_o > 0\) and \(h_i < 0\).
- Thus, \(v\) is negative (image on the left) and \(u\) is negative (object on the left).
- This statement is **correct**.

5. **Statement 3**: If the object and image are on the opposite side of the mirror.
- If the object is above the principal axis (positive height) and the image is below (negative height), we expect \(v\) to be positive (image on the right) and \(u\) to be negative (object on the left).
- This means that they cannot be on opposite sides of the mirror, making this statement **incorrect**.

6. **Statement 4**: If the object is on the principal axis, then the image lies on the principal axis.
- If the object is on the principal axis, both heights can be zero, leading to the image also being on the principal axis.
- This statement is **correct**.

### Conclusion:
The incorrect statement is **Statement 3**.