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
yx, t   r sin t  kz
• circular motion
r, where   t  kz
 r cost  kz, r sin t  kz
14
Sinusoidal waves
y
t  t0
x
yx, t   y0 sin t  kx   
at

t  t0 ,
yx, 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
yx, t   y0 sin t  kx   
at

x  x0,
yx0 , 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
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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
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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
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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
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Polarization by scattering
cdoswell.com/tips3.htm
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Brewster’s angle
r
i
i
r 
• reflected light fully (s-) polarized
cos i  sin r
1
 sin i

tan i  
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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
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