Fig. 58.
I come next to the second case, which concerns the calculation of the elements of a concentric ring. The section a b c d e ([fig. 58]) of one of those rings includes a mixtilinear triangle a b e, and a rectangle b c e d, the thickness b c being the same as that of the edge of the central disc; and the elements to be determined are the radius of the curve surface, and the position of the centre of curvature, with reference to the vertex of the lens.
Fig. 59.
The radius of curvature of the zone may be calculated by the following formulæ, in which (see [fig. 59])
r₁ = AB the distance of the outer margin of the zone from the axis of the lens
r₂ = AE the distance of the inner margin from the axis
l = BE the breadth of the zone = r₁ - r₂
ρ = the radius of curvature = b C = m C