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Waves, Light & Quanta

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Waves, Light & Quanta

Tim Freegarde

Web Gallery of Art; National Gallery, London

Circumference of the earth

(Tropic of Cancer)

Eratosthenes of Cyrene (276-195 BC)

- 5000 stadia ~ 5000 x 180m = 900 km

- α = β ~ 1/50 circle

Radius astronomicus

Reinerus Gemma-Frisius, Leuven

- measurement of celestial angular distances

Camera obscura

Reinerus Gemma-Frisius, Leuven

de radio astronomica et geometrica, 1545

- solar eclipse, 24 Jan 1544

Pinhole camera

image

object

pinhole

foil

screen

a

b

x

x

0

L

Rays

S

S

- light travels in straight lines

- shortest distance between two points

B

C

A

P

P

1.

light travels in straight lines

The nature of light

light travels between two points by the shortest distance

a

P=S

- equal angles:

b

x

x

0

L

Rays

S

S

- light travels in straight lines

- shortest distance between two points

B

C

A

P

P

P

b

a

P=S

- equal angles:

b

P

x

x

0

L

Reflection

S

S

- light travels in straight lines

- shortest distance between two points

P

P

S

P

P=S

- equal angles:

Reflection at a curved surface

- light travels in straight lines

- shortest distance between two points

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

S

S

P

P

Conic sections

focus B

focus

focus A

PARABOLA

ELLIPSE

directrix

S

P

P=S

- equal angles:

Concave mirror

- light travels in straight lines

- shortest distance between two points

f

R

- equal times to focus

Hugo of Provence

Nicholas of Rouen

Lenses and refraction

Ibn al-Haytham ‘Alhazen’

(965-1039)

Tommaso da Modena (1325-1379)

Chiesa San Nicolò, Treviso

a

b

x

x

0

L

Fermat’s principle of least time

S

S

B

C

A

P

P

- refraction at a plane surface

Pierre de Fermat (1601-1665)

a

b

x

x

0

L

Pierre de Fermat (1601-1665)

Fermat’s principle of least time

S

S

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

P

P

- refraction at a plane surface

a

b

x

x

0

L

Willebrord Snel van Royen

(Leiden, 1580-1626)

Snell’s law of refraction

S

S

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

P

P

- refraction at a plane surface

1.

light travels in straight lines

The nature of light

light travels between two points by the shortest distance

light 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