Waves, Light & QuantaTim Freegarde

Web Gallery of Art; National Gallery, London

2

Circumference of the earth

Eratosthenes of Cyrene (276-195 BC)

• 5000 stadia ~ 5000 x 180m = 900 km

• α = β ~ 1/50 circle

(Tropic of Cancer)

3

Radius astronomicus

Reinerus Gemma-Frisius, Leuven

• measurement of celestial angular distances

4

Camera obscura

• solar eclipse, 24 Jan 1544

Reinerus Gemma-Frisius, Leuven de radio astronomica et geometrica,

1545

5

Pinhole camera

foil screen

pinholeobject

image

6

Rays

• light travels in straight lines

x0 L

a

b

A B C

S

P

S

P

x

• shortest distance between two points

7

The nature of light

light travels between two points by the shortest distance

light travels in straight lines

1.

8

Rays

• light travels in straight lines

x0 L

a

b

A B C

S

P

S

P

x

• shortest distance between two points• equal angles:

P=S

9

Reflection

• light travels in straight lines

x0 L

a

b

S

P

S

P

x

• shortest distance between two points

P

bP

• equal angles:

P=S

10

Reflection at a curved surface

• light travels in straight lines

• shortest distance between two points• equal angles:

P=S

SP

• suppose we design a surface so that all routes are the same length…?

11

Conic sections

SP

directrix

focus

PARABOLA

focus Afocus B

ELLIPSE

SP

12

Concave mirror

• light travels in straight lines

• shortest distance between two points• equal angles:

P=S

SP

• equal times to focus

Rf

13

Lenses and refraction

Hugo of Provence

Nicholas of RouenTommaso da Modena (1325-

1379)Chiesa San Nicolò, Treviso

Ibn al-Haytham ‘Alhazen’(965-1039)

14

Fermat’s principle of least time

• refraction at a plane surfacePierre de Fermat (1601-1665)

x0 L

a

b

A B C

S

P

S

P

x

15

Fermat’s principle of least time

• refraction at a plane surfacePierre de Fermat (1601-1665)

x0 L

a

b

S

P

S

P

x

• light rays follow the path of least time between two points

16

Snell’s law of refraction

• refraction at a plane surface

x0 L

a

b

S

P

S

P

x

• light rays follow the path of least time between two points

• PPSS sinsin

Willebrord Snel van Royen(Leiden, 1580-1626)

17

The nature of light

light travels between two points by the shortest distancelight travels between two points by the quickest route (least time)light travels between two points by the route for which the time taken is a stationary value

light travels in straight lines

1.