A ray of light passing through the centre of curvature of a concave mirror gets reflected along the same path because when ray of light passes through centre of curvature of a concave mirror it strikes the mirror at 90 degree that is incident ray coincides normal therefore angle of incidence = 0 so, according to law of reflection angle of reflection = 0 thus ray of light retraces its path.
when the ray passes throughthe center of curvature....on the mirror it falls perpendicularrly...ie.it coincides wid normal on the piint of incidence......
according to the lawsof reflection...angle of ( incidence=reflection.)
thus applyinn this rule..if the incident ray coincides wid normal thus its distance angle 4rm it is 0o thus agle f reflection is also...0o n the reflected ray bounces back...!! hope this helps..:))