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Because a ray that passes through the center of curvature falls perpendicular to the surface (along a normal to the surface), hence it is reflected along the same path.

Q: Why is the ray passing through centre of curvature reflects along the same path?

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the centre of sphere is known as centre of curvature

the center of curvature is the ORIGIN of the radius of curvature

If the object is placed on the principal axis of a concave mirror at a point between the focus and centre of curvature the image will form beyond the centre of curvature

When it passes through optical centre.

The geometric centre of a spherical mirror is called its pole. The centre of the hollow sphere for which the mirror is a part, is called the centre of curvature. The line joining the centre of curvature and the pole is the principal axis. A light ray incident on a spherical mirror, after reflection appears to pass through the principal focus in the case of a convex mirror and passes through the focus in the case of concave mirror. The diameter of the spherical mirror gives the measure of its aperture

Related questions

define the term centre of curvature

the centre of sphere is known as centre of curvature

the center of curvature is the ORIGIN of the radius of curvature

If the object is placed on the principal axis of a concave mirror at a point between the focus and centre of curvature the image will form beyond the centre of curvature

The light ray passing from the centre of curvature is perpendicular or normal to the the sphere of which the concave mirror is a part . because the ray from centre to mirror will act as the radius and we know that radius is perpendicular to the tangent at the point of contact. hence angle of incidence = 0 degree , so angle of refraction will also be 0 degree , hence the ray will retrace its path .Read more: Why_light_ray_retrace_its_path_when_passes_through_centre_of_curvature_of_a_concave_mirror

The focal point of a convex mirror lies on the same side as the centre of curvature and is at a distance of half the radius of curvature from the optical centre.

It is the radius from the centre to the circumference or the diameter passing through the centre to both sides of the circumference

When it passes through optical centre.

No it is not a mountain. It is an imaginary line passing through the centre of the earth.

The geometric centre of a spherical mirror is called its pole. The centre of the hollow sphere for which the mirror is a part, is called the centre of curvature. The line joining the centre of curvature and the pole is the principal axis. A light ray incident on a spherical mirror, after reflection appears to pass through the principal focus in the case of a convex mirror and passes through the focus in the case of concave mirror. The diameter of the spherical mirror gives the measure of its aperture

An infinite number, all passing through the centre.

Because the center of curvature is defined to be in the direction of the normal. remember that a reflecting angle of light, relative to the normal, equals minus the angle of the beam that hit the mirror, relative to the normal. since the center of curviture is in the direction of the normal. A beam going through it would be with an angle of zero, and there for return with an angel of (minus) zero. In other words it comes back in the same direction.