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

2. 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. 3 Radius astronomicus Reinerus Gemma-Frisius, Leuven measurement of celestial angular distances

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

5. 5 Pinhole camera foil screen pinholeobject image

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

7. 7 The nature of light light travels between two points by the shortest distance light travels in straight lines1.

8. 8 Rays light travels in straight lines x 0L a b A BC S P S P x shortest distance between two points equal angles: P = S

9. 9 Reflection light travels in straight lines x 0L a b S P S P x shortest distance between two points P b P equal angles: P = S

10. 10 Reflection at a curved surface light travels in straight lines shortest distance between two points equal angles: P = S S P suppose we design a surface so that all routes are the same length…?

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

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

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

14. 14 Fermat’s principle of least time refraction at a plane surface Pierre de Fermat (1601-1665) x 0L a b A BC S P S P x

15. 15 Fermat’s principle of least time refraction at a plane surface Pierre de Fermat (1601-1665) x 0L a b S P S P x light rays follow the path of least time between two points

16. 16 Snell’s law of refraction refraction at a plane surface x 0L a b S P S P x light rays follow the path of least time between two points Willebrord Snel van Royen (Leiden, 1580-1626)

17. 17 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 light travels in straight lines1.