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.

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Waves, Light & Quanta

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Waves light quanta

Waves, Light & Quanta

Tim Freegarde

Web Gallery of Art; National Gallery, London


Circumference of the earth

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

Radius astronomicus

Reinerus Gemma-Frisius, Leuven

  • measurement of celestial angular distances


Camera obscura

Camera obscura

Reinerus Gemma-Frisius, Leuven

de radio astronomica et geometrica, 1545

  • solar eclipse, 24 Jan 1544


Pinhole camera

Pinhole camera

image

object

pinhole

foil

screen


Waves light quanta

a

b

x

x

0

L

Rays

S

S

  • light travels in straight lines

  • shortest distance between two points

B

C

A

P

P


The nature of light

1.

light travels in straight lines

The nature of light

light travels between two points by the shortest distance


Waves light quanta

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


Reflection

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


Reflection at a curved surface

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…?


Conic sections

S

S

P

P

Conic sections

focus B

focus

focus A

PARABOLA

ELLIPSE

directrix


Concave mirror

S

P

P=S

  • equal angles:

Concave mirror

  • light travels in straight lines

  • shortest distance between two points

f

R

  • equal times to focus


Lenses and refraction

Hugo of Provence

Nicholas of Rouen

Lenses and refraction

Ibn al-Haytham ‘Alhazen’

(965-1039)

Tommaso da Modena (1325-1379)

Chiesa San Nicolò, Treviso


Fermat s principle of least time

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)


Fermat s principle of least time1

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


Snell s law of refraction

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


The nature of light1

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


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