A Calculation of a Two-Lens Objective. (Second Paper)

Abstract

(1) Find the four radii by the formulae proposed by me.
(2) With these values of the radii as well as given values of thickness and interval t's, find s₁′, s₂′ and s₃′.
(3) With thege s′'s and t's, calculate ω₁, ω₂ and ω₃ [Use the formulae (I)].
(4) With the values of the radii found in (1) and with the given values of t's, calculate Q₁, Q₂, Q₃ and Q₄. [Use the definition formula of Q].
(5) Next calculate the formulae (VII).
(6) And then calculate σ₄′ by (A), Γ by (B), S by (C), T by (D), and differential coefficients by (III), (IV), (V), (VI).
(7) With these values, calculate (II) and find ΔQ₁, ΔQ₂, ΔQ₃ and ΔQ₄, putting Γ=0, S=0 and T=0.
(8) Find Q₁+ΔQ₁, Q₂+ΔQ₂, Q₃+ΔQ₃ and Q₄+ΔQ₄ by the simple addition of the values found in (4) and (7).
(9) By the aid of definition formulae of optical invariants, find corrected radii from Q₁+ΔQ₁, Q₂+ΔQ₂, Q₃+ΔQ₃ and Q₄+ΔQ₄.