i. Unlike spherical shape, every point on a parabola is equidistant from a straight line and a point.
ii. Consider given parabola having RS as directrix and F as the focus. Points A, B, C on it are equidistant from line RS and point F.
iii. Hence A’A = AF, B’B = BF, C’C = CF, and so on.
iv. If rays of equal optical path converge at a point, that point is the location of real image corresponding to that beam of rays.
v. From figure, the paths A”AA’, B”BB’. C”CC’, etc., are equal paths when mirror is neglected.
vi. If the parabola ABC is a mirror then by definition of parabola the respective optical paths,
A”AF = B”BF = C”CF
vii. Thus, F is the single point focus for entire beam of rays parallel to the axis and there is no spherical aberration.
Hence, parabolic mirrors are preferred over spherical one as there is no spherical aberration.