Waves, Light & QuantaTim Freegarde

Web Gallery of Art; National Gallery, London

2

Ray propagation

• follow ray through optical elements

F F

• characterize ray by andyz

y

d

d

y

yz

• divide system into elements

• assume linear mapping of input to output, e.g.

112 d

d

z

ybyay

1 2

3

Ray propagation

1 2

• free space

112 d

d

z

ytyy

t12 d

d

d

d

z

y

z

y

1 2

• refraction 12 yy 12

1

2 d

d

d

d

z

y

z

y

1 2

• thin lens 12 yy f

y

z

y

z

y 1

12 d

d

d

d

4

Ray propagation matrices

then

12

dd

dd

ydc

ba

yzy

zy

• if 11

2 d

dyd

z

ycy

1

12 d

d

d

dyb

z

ya

z

y

and

• for many elements,

111

11

22

22

11

11 dd

dd

ydc

ba

dc

ba

dc

ba

yzy

zy

nn

nn

n

1

dd

yDC

BAzy

5

Ray propagation matrices - II

then

12

dd

dd

ydc

ba

yzy

zy

• if 11

12 d

dyd

z

ycy

1

11

22 d

d

d

dyb

z

ya

z

y

and

• for many elements,

111

11

22

22

11

11 dd

dd

ydc

ba

dc

ba

dc

ba

yzy

zy

nn

nn

n

1

dd

yDC

BAzy

6

Ray propagation matrices

1 2

• free spacet

1 2

• refraction

1 2

• thin lens

12

dd

dd

1

01

yyzy

ηtz

y

12

dd

dd

10

01

yyzy

zy

12

dd

dd

10

1

yyzy

fzy

Waves, Light & QuantaTim Freegarde

Web Gallery of Art; National Gallery, London

8

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)

9

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)

10

Colour

Methuselah (C12)Canterbury Cathedral

Magi and Herod (C12-13)Canterbury Cathedral

11

The prism

12

Colour

Waves, Light & QuantaTim Freegarde

Web Gallery of Art; National Gallery, London

14

The prism

15

Rainbows

16

Rainbows

i

i

i

r

r

r

rx rr

17

Rainbows

i

i

i

r

r

r

rx rr

18

Rainbows

i

i

i

r

r

r

rx rr

19

Rainbows

20

Rainbows

21

Rainbows