A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For...
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![Page 1: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/1.jpg)
A
Why do metals reflect so well?
Optical properties of a conductor
Modification for conductor: 2 0o
2 e e
e e
i k r t i k r t
o o o
q qr r r E e r r E e
m m
For bound charges, the spring limits the displacement r
What limits r for free charges?
![Page 2: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/2.jpg)
displacement r for bound, unbound charges
0 0.5 1 1.5 2 2.5-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5x 10
-6
(1016 rad/sec)
disp
lace
men
t xo
magnitude
real
imaginary
![Page 3: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/3.jpg)
A
Optical properties of a conductor
2
2
2 2
11 1 e
e o o
q Nn i
m i
First, start with (opposite case!) of dielectric: (insulator)
Modification for conductor:
2
2
21 1 pn i
i
2 0o
![Page 4: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/4.jpg)
Typical plasma frequencies density N (m-3) (Hz)
metals 1028 1016
semicond. (pure) 1024 1014
semicond. (doped), fusion expts
1020 1012
ionosphere (60 to 450 km)
1011 107
interplanetary space
107 105
p
22 ep
e o
q N
m
![Page 5: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/5.jpg)
A
Optical properties of a conductor
2
2
21 pn i
Case of very little damping << :g w
22 2
22 1 pn in
For < w wp , check the sign of . Which must be nonzero?
a) n b) k
2 0in ?2
21 p
![Page 6: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/6.jpg)
A
Optical properties of a conductor
Since wo 0, can we simply shift n( ), ( )?w k w
![Page 7: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/7.jpg)
n,k for metal. Plasma frequency divides two regimes
A
g=wp/10
g=0n, k
g=wp/10
n, k
Which frequencies are transmitted well?Which are reflected well?
![Page 8: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/8.jpg)
Reflectance vs. Wavelength
Plasma frequency of silver
![Page 9: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/9.jpg)
Poynting Vectorenergy density in a vacuum
field mediumS u ut
2 20
02 2fieldE B
u
o
BS E
What equation does this look like?
Its magnitude is the intensity: Power/area
So S is an energy flow vector: energy/area/time
![Page 10: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/10.jpg)
Directions of vectors
o
BS E
o
o
k EB
![Page 11: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/11.jpg)
S, irradiance, intensity
o
BS E
For a plane wave in index n, derive the time average intensity
oo
k EB
22 2 2
2
2 2
2
o otime avg o ox o y o z
oo
n c n cI E E E E
ncB
![Page 12: A Why do metals reflect so well? Optical properties of a conductor Modification for conductor: For bound charges, the spring limits the displacement r.](https://reader036.fdocuments.in/reader036/viewer/2022062320/56649f3e5503460f94c5f3af/html5/thumbnails/12.jpg)
o
BS E
o
o
k EB
The following are always true (definition and basic MaxEqn for plane wave)
Which vector pair is not guaranteed to be perpendicular? a) E, Sb) E, kc) E, Bd) S, Ee) B, k
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Preview:
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P. is a solution to
It is also a solution to ____:1)
2)
a) eqn 1b) eqn 2c) bothd) neither
Wave equation
f x t f x ct ( , ) ( )2 2
2 2 2
10
f x tf x t
x c t
( , )
( , )
3 3
3 3 3
10
f x tf x t
x c t
( , )
( , )
4 4
4 4 4
10
f x tf x t
x c t
( , )
( , )