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 3 Circumference of the earth Eratosthenes of Cyrene ( BC) 5000 stadia ~ 5000 x 180m = 900 km α = β ~ 1/50 circle

4 Radius astronomicus Reinerus Gemma-Frisius, Leuven measurement of celestial angular distances

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

6 Pinhole camera foil screen pinholeobject image

7 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

8 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

9 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…?

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

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

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

13 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

14 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

15 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, )

16 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.

17 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, )

18 Refraction at a curved surface θ1θ1 θ2θ2 C R l1l1 l2l2 η1η1 η2η2 s1s1 s2s2 P S h no dependence upon h small angle approximation etc.

19 Refraction at a curved surface η1η1 η2η2 s1s1 s2s2 θ1θ1 θ2θ2 R l1l1 l2l2 h P SC no dependence upon h all rays from S arrive at P small angle approximation etc.

20 Refraction at a curved surface η2η2 s1s1 s2s2 P SC η1η1 no dependence upon h all rays from S arrive at P small angle approximation etc. object points S mapped to image points P S′ P′

21 Refraction at a curved surface η2η2 s1s1 s2s2 P SC η1η1 S′ P′

22 Refraction at a curved surface η2η2 s1s1 s2s2 S η1η1 P C

23 The thin lens s1s1 -s 2 p1p1 p2p2 S2S2 S1S1 P2P2 ηBηB ηAηA ηAηA

24 The thin lens s1s1 S2S2 S1S1 P2P2 s p S P -s 2 p1p1 p2p2 Lensmaker’s formula: ηBηB ηAηA ηAηA

25 Principles of imaging S lenses can affect only the apparent position of an observed object P rays from the focus are collimated parallel rays converge on the focus central rays are not deviated a lens is characterized by its focal length or power (dioptres)