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

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2 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)

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3 Principles of imaging S REAL OBJECT S VIRTUAL OBJECT P REAL IMAGE VIRTUAL IMAGE P

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4 Imaging sign conventions REAL IS POSITIVE object distance image distance lens power surface radius of curvature from object to lens from lens to image converging positive from surface to centre LENSES converging (biconvex) diverging (biconcave) f positive f negative

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5 Lens system analysis RAY TRACING RULES rays from the focus are collimated parallel rays converge on the focus central rays are not deviated OBJECT AND IMAGE DISTANCES RAY TRANSFER MATRICES

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6 Ray propagation follow ray through optical elements F F characterize ray by and y y z divide system into elements assume linear mapping of input to output, e.g. 12

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7 Ray propagation 1 2 free space t 1 2 refraction 1 2 thin lens

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8 Ray propagation matrices then if and for many elements,

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9 Ray propagation matrices - II then if and for many elements,

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10 Ray propagation matrices 1 2 free space t 1 2 refraction 1 2 thin lens

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11 Rays of light Jan Van Eyck (c1395-1441) National Gallery of Art (c1434) Fra Angelico (c1387-1455) Museo del Prado (c1430) Carlo Crivelli (c1435-1495) Städel, Frankfurt (c1482)

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12 Colour Wilton Diptych (c1395-9) National Gallery ultramarine:lapis lazuli sulphur (S 3 - ) Azzurro oltramarino si è un colore nobile, bello, perfettissimo oltre a tutti i colori; del quale non se ne potrebbe né dire né fare quello che non ne sia più. E per la sua eccellenza ne voglio parlare largo, e dimostrarti appieno come si fa. E attendici bene, però che ne porterai grande onore e utile. Ultramarine blue is a colour that is noble, beautiful, the most utterly perfect of all colours; of which one can neither say nor do anything that it would not surpass. And because of its excellence, I wish to speak of it at length, and show you in detail how to make it. And pay attention, because it will bring you great honour and usefulness. Il libro dell’arte (The Craftsman’s Handbook) Cennino D' Andrea Cennini (~1400) electronic absorption 600 nm (red)

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13 Colour Methuselah (C12) Canterbury Cathedral Magi and Herod (C12-13) Canterbury Cathedral

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14 The prism

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15 Colour

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16 Rainbows

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17 Rainbows

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Geometric Optics: Mirrors and Lenses. Mirrors with convex and concave spherical surfaces. Note that θ r = θ i for each ray.

Geometric Optics: Mirrors and Lenses. Mirrors with convex and concave spherical surfaces. Note that θ r = θ i for each ray.

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