Newton's Work on Geometrical Optical Aberrations

Abstract

IN Newton's “Opticks” (editions of 1704, 1717 and 1721 and the subsequent editions and translations, so far as we have been able to ascertain) an erroneous condition is given for the proportion α of the radii of a symmetrical thin triplet (the inner lens being of water) in order to correct the system for spherical aberration for distant objects. Calling the curvature of the first and second surface R₁ and R₂ respectively, the formula gives α³ = (R₁/R₂)³ = (KK–KI)/(RK–RI), where R/I = n_g, the refractive index of the two outer (glass) lenses, and R/K = n_w, the refractive index of the inner (water) lens. The fraction can be simplified to K/R, and gives a large amount of under-correction.