Waves, Light & Quanta
Tim Freegarde
Web Gallery of Art; National Gallery, London
Principles of imaging
• lenses can affect only the apparent
position of an observed object
• rays from the focus are collimated
• parallel rays converge on the focus
• central rays are not deviated
• a lens is characterized by its
• focal length f or
•
power D  1 f (dioptres)
P
S
2
Principles of imaging
REAL IMAGE
REAL OBJECT
S
P
VIRTUAL
OBJECT
S
VIRTUAL
IMAGE
P
3
Imaging sign conventions
REAL IS POSITIVE
• object distance
• from object to lens
• image distance
• from lens to image
• lens power
• converging positive
• surface radius of curvature
• from surface to centre
LENSES
• converging (biconvex)
• f positive
1 1 1
 
s p f
• diverging (biconcave)
•f
negative
4
Lens system analysis
RAY TRACING RULES
• rays from the focus are collimated
• parallel rays converge on the focus
• central rays are not deviated
OBJECT AND IMAGE DISTANCES
1 1 1
 
s p f
RAY TRANSFER MATRICES
5
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
6
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
7
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   an1 bn1   a2
 dz   

 y  c
  n  n 1 d n1   c2
b2   a1 b1   dy 
 
  dz 
d 2   c1 d1   y 1
 A B   dy 
  dz 
 
 C D   y 1
8
Ray propagation matrices - II
• if
 dy 
 dy 
2    a1    b y1
 dz  2
 dz 1
then
and
 dy 
y2  c1    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  n1 d n 1   c2
b2   a1 b1   dy 
 
  dz 
d 2   c1 d1   y 1
 A B    dy 
  dz 
 
 C D   y 1
9
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
10
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)
11
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
12
Colour
Magi and Herod (C12-13)
Canterbury Cathedral
Methuselah (C12)
Canterbury Cathedral
13
The prism
14
Colour
15
Rainbows
16
Rainbows
17