Transcript Reflection/Transmission Snell`s Laws

Ray Tracing
Reflection/Transmission
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Ray Tracing
Reflection/Transmission
n2
n1
qt
qi qr
qi = qr
sin(qi)/sin(qt) = n2/n1
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Snell’s Laws (1621)
Reflection/Transmission
qi = qr
sin(qi)/sin(qt) = n2/n1
Willebrord Snell
n2
n1
qt
qiqr
Entering dense medium: bend towards normal
Leaving dense medium: bend away from normal
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Light
bends because it’s slowed down
Reflection/Transmission
Picture courtesy
Joseph F. Alward, Physics,
University of the Pacific
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Deriving Snell’s law
Reflection/Transmission
Multiple wavefronts arrive
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Deriving Snell’s law
Reflection/Transmission
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Deriving Snell’s law
Reflection/Transmission
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Deriving Snell’s law
Reflection/Transmission
The incident waves set the
interfacial atoms oscillating,
which re-radiate this energy
as spherical waves
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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
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Deriving Snell’s law
Reflection/Transmission
Many spherical waves
conspire to create a new set
of reflected and transmitted
plane waves
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Deriving Snell’s law
Reflection/Transmission
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Deriving Snell’s law
Reflection/Transmission
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Deriving Snell’s law
Reflection/Transmission
Time for incident wave to cover
Time for reflected wave
= Lsinqr/v1
qi L
qt
this distance = Lsinqi/v1
qr
Time for
transmitted wave
= Lsinqt/v2
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Deriving Snell’s law
Reflection/Transmission
Lsinqi/v1 = Lsinqr/v1 = Lsinqt/v2
qi L
qt
 Snell’s Law
qr
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Fun examples of refraction
Reflection/Transmission
Picture courtesy
Joseph F. Alward, Physics,
University of the Pacific
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Fun examples of refraction
Reflection/Transmission
Apparent depth
Distorted objects
Rainbow
Mirage
Pictures courtesy
Joseph F. Alward homepage, Physics,
University of the Pacific
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Physics of Rainbows
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Physics of Rainbows
Crucial physics: violet bends more than red
Red on top !
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Double Rainbows
Supernumerary rainbow: colors reversed
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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
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Why does violet bend more?
+
-
Snapshot of
e tied to nucleus
.. .
m(x+gx+w02x) = qEejwt
P= nqx = nq2E/m(w02-w2-jgw)
e = D/E = e0 + P/E
e = e0[1+ wp2/(w02-w2-jgw)]
wp = (Nq2/me0)
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Recall plasma frequency
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
e = e0[1- wp2/w2) ]
wp = (Nq2/me0)
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Why does violet bend more?
e = e0[1+ wp2/(w02-w2-jgw)]
Near resonance w0 expect peak in e’’
Re(e) becomes negative, so no wave propagates
Propagation resumes after w > wp
Crown glass
-Im(e)
Re(e)
w0
wp
w
Salmon DNA
(Globus et al)
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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)
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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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