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angle angular aperture apply astigmatism auxiliary axis axial pencil becomes bending biconvex lens calculation colours coma Coma's components computing conjugate corresponding crown curvature determined diagram diameter diaphragm difference disk distance distortion entrance pupil equation exit pupil extra-axial eyepiece field final finite focal length focal line focus formulae full aperture gives glass graph hence image-plane image-point inch intersection-lengths Lagrange's theorem last surface lens system lenses linear magnification marginal ray method microscope negative numerical object-glass object-point oblique pencil obtain optical axis P-values parabola paraxial ray Petzval positive primary aberration principal ray radius Ramsden Ramsden eyepiece ratio ray-tracing reference refracting surface refractive index result sagittal rays second surface Seidel Aberrations semi-aperture simple simple lens sine theorem solution spherical aberration tangential telescope objectives term thickness thin lens tion traced transverse chromatic aberration trigonometrical usual whilst zero zone