The distance from the pole to the center of curvature is called (no surprise, I hope) the radius of curvature (r). The distance from the pole to the focal point is called the focal length (f). The focal length of a spherical mirror is then approximately half its radius of curvature.

Difference between Pole of Spherical Mirror and Center of Curvature

The pole of a spherical mirror and the center of curvature are two important points associated with a curved mirror. Let's understand the difference between these two points in detail:

1. Pole of Spherical Mirror:
- The pole of a spherical mirror is the geometric center of the mirror's surface.
- It is the point where the principal axis intersects the mirror.
- The pole is denoted by the letter 'P' in the ray diagrams.
- It is also the point where incident rays parallel to the principal axis converge or diverge after reflection.
- In a concave mirror, the pole lies on the reflective surface facing the incoming light rays.
- In a convex mirror, the pole lies on the backside of the mirror surface.

2. Center of Curvature:
- The center of curvature is the center of the sphere from which the curved mirror is formed.
- It is denoted by the letter 'C' in the ray diagrams.
- The center of curvature is located on the principal axis, exactly opposite to the mirror's pole.
- It is equidistant from every point on the mirror's surface.
- For a concave mirror, the center of curvature lies in front of the mirror.
- For a convex mirror, the center of curvature lies behind the mirror.
- The radius of curvature is the distance between the pole and the center of curvature.

Key Differences:
- The pole is the point where the principal axis intersects the mirror, while the center of curvature is the center of the sphere from which the mirror is formed.
- The pole lies on the reflective surface of the mirror, whereas the center of curvature is located on the principal axis, exactly opposite to the pole.
- The pole is the point where incident rays parallel to the principal axis converge or diverge after reflection, while the center of curvature is not directly involved in the reflection process.
- The pole and the center of curvature are equidistant from each other in a spherical mirror.
- The distance between the pole and the center of curvature is the radius of curvature.
- The pole is denoted by 'P', and the center of curvature is denoted by 'C' in the ray diagrams.

Conclusion:
In summary, the pole of a spherical mirror is the point where the principal axis intersects the mirror's surface, while the center of curvature is the center of the sphere from which the mirror is formed. The pole is involved in the reflection process, whereas the center of curvature is not directly involved but is important in determining the mirror's properties.