Waves, Light & QuantaTim Freegarde

Web Gallery of Art; National Gallery, London

2

Rays of light

Jan Van Eyck (c1395-1441)National Gallery of Art (c1434)

Fra Angelico (c1387-1455)Museo del Prado (c1430)

Carlo Crivelli (c1435-1495)Städel, Frankfurt (c1482)

3

Colour

Wilton Diptych (c1395-9)National Gallery

• ultramarine: lapis lazuli

sulphur (S3-)

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.

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.

Il libro dell’arte (The Craftsman’s Handbook)

Cennino D' Andrea Cennini (~1400)

electronic absorption 600 nm

(red)

4

Colour

Methuselah (C12)Canterbury Cathedral

Magi and Herod (C12-13)Canterbury Cathedral

5

The prism

6

Colour

7

Rainbows

8

Rainbows

i

i

i

r

r

r

rx rr

9

Rainbows

i

i

i

r

r

r

rx rr

10

Rainbows

i

i

i

r

r

r

rx rr

11

Rainbows

12

Rainbows

13

Rainbows

14

Sinusoidal waves

kztrtxy sin,

• simple harmonic motion

• circular motion

,r kzt where

kztrkztr sin,cos

z

15

Sinusoidal waves

0tt

0tt at ,

• wavenumber

2k

x

y

000 sin, tkxytxy

• spectroscopists’

1~ wavenumb

er

00~2sin txy

00

2sin txy

• wavelength

kxtytxy sin, 0

16

Sinusoidal waves

0xx

0xx at ,

• angular frequency

2

t

y

000 sin, kxtytxy

• frequency

1 00 2sin kxty

00

2sin kxty

• period

kxtytxy sin, 0

17

Birefringence

• asymmetry in crystal structure causes two different refractive indices

• opposite polarizations follow different paths through crystal

• birefringence, double refraction

18

Optical polarization

• for any wavevector, there are two field components

• light is a transverse wave: perpendicular to E k

• any wave may be written as a superposition of the two polarizations

19

Linear dichroism

• conductivity of wire grid depends upon field polarization

• electric fields perpendicular to the wires are transmitted

WIRE GRID POLARIZER

• fields parallel to the wires are absorbed

20

Malus’ law

WIRE GRID POLARIZER

• amplitude transmission

cos

• intensity transmission

2cos

21

Linear dichroism

• crystals may similarly show absorption which depends upon linear polarization• absorption also depends upon wavelength• polarization therefore determines crystal colour

TOURMALINE

• pleochroism, dichroism, trichroism

22

Polarization in nature

• the European cuttlefish also has polarization-sensitive vision

• … and can change its colour and polarization!

MAN’S VIEW CUTTLEFISH VIEW (red = horizontal polarization)

CUTTLEFISH (sepia officinalis)

23

Circular dichroism

• absorption may also depend upon circular polarization

• the scarab beetle has polarization-sensitive vision, which it uses for navigation

• the beetle’s own colour depends upon the circular polarization SCARAB BEETLE LEFT CIRCULAR

POLARIZED LIGHT

RIGHT CIRCULAR

POLARIZED LIGHT

24

Optical activity (circular birefringence)

l-limonene(orange)

r-limonene(lemon)

CH2

CH3

HCH3 CH2

CH3

HCH3

CHIRAL MOLECULES

• 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

25

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

26

Polarization notation

• circular polarization• right- or left-handed rotation

when looking towards source

• linear (plane) polarization• parallel or perpendicular to

plane of incidence

RCP plane of incidence

perpendicular

parallel

• traces out opposite (right- or left-) handed thread

• plane of incidence contains wavevector and normal to surface

27

Polarization by scattering

cdoswell.com/tips3.htm

28

Brewster’s angle

ir

ri sincos

i

sin1

itan

• reflected light fully (s-) polarized

ir

29

Brewster’s angle

www.paddling.net/sameboat/archives/sameboat496.html

ii

r

r

itan• reflected light fully (s-) polarized

30

sin,cos iea

Characterizing the optical polarization

• wavevector insufficient to define electromagnetic wave• we must additionally define the polarization vector

k

yx aa ,ax

y

z

sin,cosa• e.g. linear polarization at

angle