Let 0 be the centre of the spherical surface of the mirror, ABC the ray incident at a distance BE from the mirror axis, and OB = R (Fig. 244).
From the right triangle OBE, we find that sin α = h/R. The triangle OBC is isosceles since ∠ABO = ∠OBC according to the law of reflection, and ∠BOC = ∠ABO as alternate-interior angles. Hence OD = DB = R/2. From the triangle ODC, we obtain
(C is the point of intersection of the ray reflected by the mirror and the optical axis).
For a ray propagating at a distance h1, the distance x1 ≈ R/2, with an error of about 0.5% since h12 << R2. For a ray propagating at a distance h2, the distance x2 = 3.125 cm. Finally, we obtain