Waves, Light & Quanta

1. Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

2. 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) Rays of light

3. ultramarine: lapis lazuli Wilton Diptych (c1395-9) National Gallery 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 per la sua eccellenza ne voglio parlare largo, e dimostrarti appieno come si fa. E attendici bene, però che ne porterai grande onore e utile. sulphur (S3-) Colour 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.

4. Colour Magi and Herod (C12-13) Canterbury Cathedral Methuselah (C12) Canterbury Cathedral

5. The prism

6. Colour

7. Rainbows

8. x i r r i r Rainbows r r  r i

9. x i r r i r Rainbows r r  r i

10. x i r r i r Rainbows r r  r i

11. Rainbows 

12.  Rainbows

13. Rainbows

14.  where Sinusoidal waves z • simple harmonic motion • circular motion

15. wavenumber • spectroscopists’ at , wavenumber • wavelength Sinusoidal waves

16. angular frequency • frequency • period Sinusoidal waves at ,

17. asymmetry in crystal structure causes two different refractive indices • opposite polarizations follow different paths through crystal Birefringence • birefringence, double refraction

18. light is a transverse wave: perpendicular to Optical polarization • for any wavevector, there are two field components • any wave may be written as a superposition of the two polarizations

19. conductivity of wire grid depends upon field polarization • electric fields perpendicular to the wires are transmitted Linear dichroism • fields parallel to the wires are absorbed WIRE GRID POLARIZER

20. Malus’ law • amplitude transmission • intensity transmission WIRE GRID POLARIZER

21. crystals may similarly show absorption which depends upon linear polarization • absorption also depends upon wavelength • polarization therefore determines crystal colour Linear dichroism • pleochroism, dichroism, trichroism TOURMALINE

22. CUTTLEFISH (sepia officinalis) MAN’S VIEW CUTTLEFISH VIEW • the European cuttlefish also has polarization-sensitive vision • … and can change its colour and polarization! Polarization in nature (red = horizontal polarization)

23. SCARAB BEETLE LEFT CIRCULAR POLARIZED LIGHT RIGHT CIRCULAR POLARIZED LIGHT • absorption may also depend upon circular polarization • the scarab beetle has polarization-sensitive vision, which it uses for navigation Circular dichroism • the beetle’s own colour depends upon the circular polarization

24. CH3 CH3 CH3 CH3 CH2 CH2 H H • optical activity is birefringence for circular polarizations • an asymmetry between right and left allows opposing circular polarizations to have differing refractive indices Optical activity (circular birefringence) l-limonene (orange) r-limonene (lemon) • optical activity rotates the polarization plane of linearly polarized light CHIRAL MOLECULES • may be observed in vapours, liquids and solids

25. linear (plane) polarization • non-equal components in phase Categories of optical polarization • circular polarization • equal components 90° out of phase • elliptical polarization • all other cases

26. circular polarization RCP plane of incidence • right- or left-handed rotation when looking towards source perpendicular • traces out opposite (right- or left-) handed thread Polarization notation parallel • linear (plane) polarization • parallel or perpendicular to plane of incidence • plane of incidence contains wavevector and normal to surface

27. Polarization by scattering cdoswell.com/tips3.htm

28. Brewster’s angle • reflected light fully (s-) polarized

29. www.paddling.net/sameboat/archives/sameboat496.html Brewster’s angle • reflected light fully (s-) polarized

30. e.g. linear polarization at angle • wavevector insufficient to define electromagnetic wave • we must additionally define the polarization vector Characterizing the optical polarization