Ray Tracing ReflectionTransmission 1 Ray Tracing ReflectionTransmission n

Ray Tracing Reflection/Transmission 1

Ray Tracing Reflection/Transmission n 2 n 1 qt qi qr qi = qr sin(qi)/sin(qt) = n 2/n 1 2

Snell’s Laws (1621) Reflection/Transmission qi = qr sin(qi)/sin(qt) = n 2/n 1 Willebrord Snell n 2 n 1 qt qiqr Entering dense medium: bend towards normal Leaving dense medium: bend away from normal 3

Light bends because it’s slowed down Reflection/Transmission Picture courtesy Joseph F. Alward, Physics, University of the Pacific 4

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Deriving Snell’s law Reflection/Transmission Multiple wavefronts arrive 6

Deriving Snell’s law Reflection/Transmission 7

Deriving Snell’s law Reflection/Transmission 8

Deriving Snell’s law Reflection/Transmission The incident waves set the interfacial atoms oscillating, which re-radiate this energy as spherical waves 9

Deriving Snell’s law Reflection/Transmission The incident waves set the interfacial atoms oscillating, which re-radiate this energy as spherical waves The speeds (and thus the radii) of the spherical wavefronts are different in the two media 10

Deriving Snell’s law Reflection/Transmission Many spherical waves conspire to create a new set of reflected and transmitted plane waves 11

Deriving Snell’s law Reflection/Transmission 12

Deriving Snell’s law Reflection/Transmission 13

Deriving Snell’s law Reflection/Transmission Time for incident wave to cover Time for reflected wave = Lsinqr/v 1 r q in qi Ls in Ls q Lsin t qi L qt this distance = Lsinqi/v 1 qr Time for transmitted wave = Lsinqt/v 2 14

Deriving Snell’s law Reflection/Transmission q in qi Ls in Ls q Lsin t qi L qt Snell’s Law r Lsinqi/v 1 = Lsinqr/v 1 = Lsinqt/v 2 qr 15

Fun examples of refraction Reflection/Transmission Picture courtesy Joseph F. Alward, Physics, University of the Pacific 16

Fun examples of refraction Reflection/Transmission Apparent depth Distorted objects Rainbow Mirage Pictures courtesy Joseph F. Alward homepage, Physics, University of the Pacific 17

Physics of Rainbows 18

Physics of Rainbows Crucial physics: violet bends more than red Red on top ! 19

Double Rainbows Supernumerary rainbow: colors reversed 20

Why does violet bend more? Recall that we treat e, m, s etc. as given parameters for Maxwell’s equations Need a separate set of equations to get these Simplest: Newton’s law (classical) More sophisticated: Schrodinger equation (quantum) We will next try to build a classical theory of e 21

Why does violet bend more? + - Snapshot of e tied to nucleus . . . m(x+gx+w 02 x) = q. Eejwt P= nqx = nq 2 E/m(w 02 -w 2 -jgw) e = D/E = e 0 + P/E 2/(w 2 -jgw) w e = e 0[1+ p ] 0 wp = (Nq 2/me 0) 22

Recall plasma frequency Maximum frequency at which free charges (w 0 = g =0) can still follow field and screen it (e < 0, n imaginary) Related to RC constant wp = 1/√tdampingt. RC with tdamping = 1/g, t. RC = e 0/s, s = Nq 2 tdamping/m 2/w 2) w e = e 0[1 - p ] wp = (Nq 2/me 0) 23

Why does violet bend more? 2/(w 2 -jgw) w e = e 0[1+ p ] 0 Near resonance w 0 expect peak in e’’ Re(e) becomes negative, so no wave propagates Propagation resumes after w > wp Crown glass -Im(e) Re(e) w 0 wp w Salmon DNA (Globus et al) 24

Why does violet bend more? 2/(w 2 -jgw) w e = e 0[1+ p ] 0 For w 0 = 0 (free electron), e = e 0 + js/w, s = Nq 2 t/m(1 -jwt), t = 1/g For w 0 >> w (bound electron), n = e ≈ A + Cw 2 = 1. 3246 + 3092/l 2 with l in nm This explains why violet bends more than red (for l >> d, size of scatterer) 25

Blue sky vs Red sunsets n ≈ A + B/l 2 Later, we will see that reflectivity ~ n 2 ~ 1/l 4 (Rayleigh scattering, l >> d) Explains why sky is blue, and sunsets are red Larger objects have n independent of l (Mie scattering, l ~ d) n ~ (1+wp 2/w 02)1/2 Explains why clouds are white/gray 26