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

2 Circumference of the earth Eratosthenes of Cyrene ( 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 x 0L a b A BC S P S P x shortest distance between two points equal angles: P = S

7 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

8 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…?

9 Conic sections S P directrix focus PARABOLA focus A focus B ELLIPSE S P

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

11 Lenses and refraction Hugo of ProvenceNicholas of Rouen Tommaso da Modena ( ) Chiesa San Nicolò, Treviso Ibn al-Haytham ‘Alhazen’ ( )

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

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

14 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, )