Huygens and Bernoulli's brachistochrone - Rijksuniversiteit Groningen

H&B – p.23/27Optics ctd.δsinα 1δsinα 2n 1 = 1/v 1Rα 1δα 2R ′n 2 = 1/v 2Proof: Take variation of an arbitrary path P → R → Q to P → R ′ → Q with R ′ − R = δTime difference:δn 1 sin α 1 − δn 2 sin α 2 + O(δ 2 )Optimal choice for R :n 1 sin α 1 = n 2 sin α 2QEDComment: A high school proof exists with rectangles . . .