Explanation:

A spherical mirror has a center of curvature (C) and a principal axis. The point where the principal axis intersects the mirror is called the pole (P) of the mirror. The distance between the pole and the center of curvature is the radius of curvature (R). When an object is placed in front of a spherical mirror, the distance between the object and the mirror is called the object distance (u).

The sign convention used in optics is as follows:
- Distances to the right of the pole are positive
- Distances to the left of the pole are negative
- Distances in the direction of incident light are positive
- Distances opposite to the direction of incident light are negative
- Heights above the principal axis are positive
- Heights below the principal axis are negative

Now, let's consider the case of a point object placed on the principal axis of a spherical mirror.

Heading 1: Object Distance (u)

- The object distance (u) is the distance between the object and the mirror.
- Since the object is placed on the principal axis, the distance is measured along the principal axis.
- The sign of u depends on the position of the object with respect to the pole of the mirror.

Heading 2: Position of Object

- If the object is placed to the left of the pole, then the distance is negative.
- If the object is placed to the right of the pole, then the distance is positive.

Heading 3: Principal Axis

- The principal axis is a line passing through the pole and the center of curvature.
- Since the object is placed on the principal axis, it means that the object is equidistant from the pole and the center of curvature.
- Therefore, the object distance (u) is equal to the radius of curvature (R) of the mirror.
- The radius of curvature is always positive for a spherical mirror.
- Hence, the object distance (u) is always negative when the object is placed on the principal axis of a spherical mirror.

Conclusion:

In conclusion, when a point object is placed on the principal axis of a spherical mirror, the object distance (u) is always negative. This is because the object is equidistant from the pole and the center of curvature, and the distance to the left of the pole is considered negative according to the sign convention.

As the object is always placed on the left of the mirror and distances on the left of the mirror are taken as negative. Therefore object distance is definitely negative.