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Waves, Light & Quanta

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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  1. Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

  2. 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

  3. Radius astronomicus Reinerus Gemma-Frisius, Leuven • measurement of celestial angular distances

  4. Camera obscura Reinerus Gemma-Frisius, Leuven de radio astronomica et geometrica, 1545 • solar eclipse, 24 Jan 1544

  5. Pinhole camera image object pinhole foil screen

  6. a b x x 0 L Rays S S • light travels in straight lines • shortest distance between two points B C A P P

  7. 1. light travels in straight lines The nature of light light travels between two points by the shortest distance

  8. 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

  9. 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

  10. 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…?

  11. S S P P Conic sections focus B focus focus A PARABOLA ELLIPSE directrix

  12. S P P=S • equal angles: Concave mirror • light travels in straight lines • shortest distance between two points f R • equal times to focus

  13. Hugo of Provence Nicholas of Rouen Lenses and refraction Ibn al-Haytham ‘Alhazen’ (965-1039) Tommaso da Modena (1325-1379) Chiesa San Nicolò, Treviso

  14. 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)

  15. 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

  16. 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

  17. 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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