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Reflection/Transmission

Discover the principles of Snell's Law through reflections and transmissions of light waves. Learn how light bends as it moves through different media, deriving the laws governing these phenomena and exploring fun examples of refraction like rainbows and mirages. Gain insight into the physics behind why violet bends more than red, with explanations rooted in Maxwell's equations and classical and quantum theories. Explore the behavior of light waves tied to nuclei, near resonance conditions, and the impact of wave frequency on bending behavior. Unravel the mysteries of color phenomena in the sky, from blue skies to red sunsets, cloud colors, and reflections in various scattering processes.

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Reflection/Transmission

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  1. Ray Tracing Reflection/Transmission

  2. Ray Tracing Reflection/Transmission qt n2 n1 qi = qr qi qr sin(qi)/sin(qt) = n2/n1

  3. qt n2 n1 qi = qr qi qr sin(qi)/sin(qt) = n2/n1 Snell’s Laws (1621) Reflection/Transmission Willebrord Snell Entering dense medium: bend towards normal Leaving dense medium: bend away from normal

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

  5. Reflection/Transmission Deriving Snell’s law Multiple wavefronts arrive

  6. Reflection/Transmission Deriving Snell’s law

  7. Reflection/Transmission Deriving Snell’s law

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

  9. Reflection/Transmission Deriving Snell’s law 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 wave- fronts are different in the two media

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

  11. Reflection/Transmission Deriving Snell’s law

  12. Reflection/Transmission Deriving Snell’s law

  13. Deriving Snell’s law Lsinqi Lsinqr qr qi qt Lsinqt Reflection/Transmission Time for incident wave to cover this distance = Lsinqi/v1 Time for reflected wave = Lsinqr/v1 Time for transmitted wave = Lsinqt/v2 qr L

  14. Deriving Snell’s law Lsinqi/v1 = Lsinqr/v1 = Lsinqt/v2  Snell’s Law Reflection/Transmission qr Lsinqi Lsinqr L qr qi qt Lsinqt

  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? . . . m(x+gx+w02x) = qEejwt P= nqx = nq2E/m(w02-w2-jgw) e = D/E = e0 + P/E wp = (Nq2/me0) e = e0[1+ ] wp2/(w02-w2-jgw) - + Snapshot of e tied to nucleus

  22. Recall plasma frequency wp = (Nq2/me0) e = e0[1- ] wp2/w2) Maximum frequency at which free charges (w0 = g =0) can still follow field and screen it (e < 0, n imaginary) Related to RC constant wp = 1/√tdampingtRC with tdamping = 1/g, tRC = e0/s, s = Nq2tdamping/m

  23. Why does violet bend more? e = e0[1+ ] wp2/(w02-w2-jgw) -Im(e) Re(e) w Near resonance w0 expect peak in e’’ Re(e) becomes negative, so no wave propagates Propagation resumes after w > wp Crown glass w0 wp Salmon DNA (Globus et al)

  24. Why does violet bend more? e = e0[1+ ] wp2/(w02-w2-jgw) For w0 = 0 (free electron), e = e0 + js/w, s = Nq2t/m(1-jwt), t = 1/g For w0 >> w (bound electron), n = e ≈ A + Cw2 = 1.3246 + 3092/l2 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/l2 Later, we will see that reflectivity ~ n2 ~ 1/l4 (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+wp2/w02)1/2Explains why clouds are white/gray

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