Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London Ray propagation • follow ray through optical elements • characterize ray by y and dy dz • divide system into elements • assume linear mapping of input to output, e.g. dy y2 a y1 b dz 1 y F F y z 1 2 2 Ray propagation • free space • refraction • thin lens dy dy dy y2 y1 t dz 1 dz 2 dz 1 y2 y1 y2 y1 t 1 dy 1 dy dz 2 2 dz 1 dy dy y1 dz 2 dz 1 f 2 1 2 1 2 3 Ray propagation matrices • if then dy dy a b y1 dz 2 dz 1 and dy y2 c d y1 dz 1 dy a b dy dz dz y 2 c d y 1 • for many elements, dy an1 bn1 a2 dz y c n n 1 d n1 c2 b2 a1 b1 dy dz d 2 c1 d1 y 1 A B dy dz C D y 1 4 Ray propagation matrices - II • if dy dy 2 a1 b y1 dz 2 dz 1 then and dy y2 c1 d y1 dz 1 dy a b dy dz dz y 2 c d y 1 • for many elements, dy an 1 bn 1 a2 dz y c n n1 d n 1 c2 b2 a1 b1 dy dz d 2 c1 d1 y 1 A B dy dz C D y 1 5 Ray propagation matrices • free space • refraction • thin lens dy 1 0 dy dz dz t y 1 y η 2 1 t 1 dy 1 0 dy dz dz y 2 0 1 y 1 dy 1 f dy dz dz y y 0 1 2 1 2 1 2 1 2 6 Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London Rays of light Fra Angelico (c1387-1455) Museo del Prado (c1430) Carlo Crivelli (c1435-1495) Städel, Frankfurt (c1482) Jan Van Eyck (c1395-1441) National Gallery of Art (c1434) 8 Colour Azzurro oltramarino si è un colore nobile, bello, perfettissimo oltre a tutti i colori; del quale non se ne potrebbe né dire né fare quello che non ne sia più. E • ultramarine: lapis parlare lazulilargo, e per la sua eccellenza ne voglio dimostrarti appieno come si fa. E attendici - bene, sulphur (S però che ne porterai grande onore e utile. 3) Il libro dell’arte (The Craftsman’s Handbook) Cennino D' Andrea Cennini (~1400) electronic absorption 600 nm (red) Ultramarine blue is a colour that is noble, beautiful, the most utterly perfect of all colours; of which one can neither say nor do anything that it would not surpass. And because of its excellence, I wish to speak of it at length, and show you in detail how to make it. And pay attention, because it will bring you great honour and usefulness. Wilton Diptych (c1395-9) National Gallery 9 Colour Magi and Herod (C12-13) Canterbury Cathedral Methuselah (C12) Canterbury Cathedral 10 The prism 11 Colour 12 Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London The prism 14 Rainbows 15 Rainbows i r x r r r r i r i 16 Rainbows i r x r r r r i r i 17 Rainbows i r x r r r r i r i 18 Rainbows 19 Rainbows 20 Rainbows 21