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Reflection/Transmission

Ray Tracing. Reflection/Transmission. Ray Tracing. Reflection/Transmission. q t. n 2. n 1. q i = q r. q i. q r. sin( q i )/sin( q t ) = n 2 /n 1. q t. n 2. n 1. q i = q r. q i. q r. sin( q i )/sin( q t ) = n 2 /n 1. Snell ’ s Laws (1621). Reflection/Transmission.

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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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