Definition

If incident ray is parallel to the principal axis, then the reflected ray passes through focus.
If the incident ray passes through focus, then the reflected ray will be parallel to the principal axis.
If the incident ray is passed through the centre of curvature, it will reflect back the same way Why? Because it is the normal.
If the incident ray strikes the pole then the it reflects obliquely, making the principal axis the normal and angle of incidence = angel of reflection.

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What are the rules of image formation in spherical mirrors?

If incident ray is parallel to the principal axis, then the reflected ray passes through focus.
If the incident ray passes through focus, then the reflected ray will be parallel to the principal axis.
If the incident ray is passed through the centre of curvature, it will reflect back the same way
If the incident ray strikes the pole then the it reflects obliquely, making the principal axis the normal and angle of incidence = angel of reflection.

Why does the reflected ray comes back the same way as the incident ray when passed through the centre of curvature?;;Because it becomes the normal.