Transcript wlq4
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) 2 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 3 Colour Magi and Herod (C12-13) Canterbury Cathedral Methuselah (C12) Canterbury Cathedral 4 The prism 5 Colour 6 Rainbows 7 Rainbows i r x r r r r i r i 8 Rainbows i r x r r r r i r i 9 Rainbows i r x r r r r i r i 10 Rainbows 11 Rainbows 12 Rainbows 13 Sinusoidal waves z • simple harmonic motion yx, t r sin t kz • circular motion r, where t kz r cost kz, r sin t kz 14 Sinusoidal waves y t t0 x yx, t y0 sin t kx at t t0 , yx, t0 y0 sin kx t0 y0 sin 2 ~ x t0 2 y0 sin x t0 • wavenumber • spectroscopists’ wavenumber • wavelength k 2 1 ~ 15 Sinusoidal waves y x x0 t yx, t y0 sin t kx at x x0, yx0 , t y0 sin t kx0 • angular frequency y0 sin 2 t kx0 • frequency 2 y0 sin t kx0 • period 2 1 16 Birefringence • asymmetry in crystal structure causes two different refractive indices • opposite polarizations follow different paths through crystal • birefringence, double refraction 17 Optical polarization • light is a transverse wave: E perpendicular to k • for any wavevector, there are two field components • any wave may be written as a superposition of the two polarizations 18 Linear dichroism • conductivity of wire grid depends upon field polarization • electric fields perpendicular to the wires are transmitted • fields parallel to the wires are absorbed WIRE GRID POLARIZER 19 Malus’ law • amplitude transmission cos • intensity transmission cos 2 WIRE GRID POLARIZER 20 Linear dichroism • crystals may similarly show absorption which depends upon linear polarization • absorption also depends upon wavelength • polarization therefore determines crystal colour • pleochroism, dichroism, trichroism TOURMALINE 21 Polarization in nature • the European cuttlefish also has polarization-sensitive vision CUTTLEFISH (sepia officinalis) • … and can change its colour and polarization! MAN’S VIEW CUTTLEFISH VIEW (red = horizontal polarization) 22 Circular dichroism • absorption may also depend upon circular polarization • the scarab beetle has polarizationsensitive vision, which it uses for navigation • the beetle’s own colour depends upon the circular polarization SCARAB BEETLE LEFT CIRCULAR RIGHT CIRCULAR POLARIZED LIGHT POLARIZED LIGHT 23 Optical activity (circular birefringence) • optical activity is birefringence for circular polarizations • an asymmetry between right and left allows opposing circular polarizations to have differing refractive indices • optical activity rotates the polarization plane of linearly polarized light • may be observed in vapours, liquids and solids CH3 CH2 CH3 CH3 CH3 H l-limonene (orange) H CH2 r-limonene (lemon) CHIRAL MOLECULES 24 Categories of optical polarization • linear (plane) polarization • non-equal components in phase • circular polarization • equal components 90° out of phase • elliptical polarization • all other cases 25 Polarization notation • circular polarization • right- or left-handed rotation when looking towards source • traces out opposite (right- or left-) handed thread RCP plane of incidence perpendicular parallel • linear (plane) polarization • parallel or perpendicular to plane of incidence • plane of incidence contains wavevector and normal to surface 26 Polarization by scattering cdoswell.com/tips3.htm 27 Brewster’s angle r i i r • reflected light fully (s-) polarized cos i sin r 1 sin i tan i 28 Brewster’s angle i i r www.paddling.net/sameboat/archives/sameboat496.html r • reflected light fully (s-) polarized tan i 29 Characterizing the optical polarization • wavevector insufficient to define electromagnetic wave • we must additionally define the polarization vector a ax , a y • e.g. linear polarization at angle i a cos, esin sin k x z y 30