The circular boundary of the concave mirror subtends a cone of half angle $\theta$ at its centre of curvature. The minimum value of  $\theta$ for which ray incident on this mirror parallel to the principle axis suffers reflection more than one is  

If $\mathrm{\theta }={45}^0$ the given ray falling on mirror at A reflects and falls vertically on the other extreme point B of the mirror and second reflection just takes place.$\text{ If }\mathrm{\theta }>{45}^{\circ }\text{, }$ i.e. if the mirror is larger, the reflected ray falls on mirror between A and B and second reflection takes place. If the mirror is smaller, $\theta$ will be less than 45°, the ray reflected at A does not fall on mirror again and there will be only one reflection.