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Know your numbers and relations for
visible light! |
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For the propagation of
light:
use the wave model
For the generation and disappearance (=
absorption) of light:
use the photon model
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Snellius law:
n = sina/sinb with a, b the angle of incidence
or propagation, resp. |
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Wavelengths: l » 400 nm - 800
nm. |
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lmat =
l0/n. |
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Frequency: n» 10 15 Hz. |
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Index of refraction: n =
er½ » 1,5 - 2,5 |
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Energy E
» 1,8 eV - 3,2 eV. |
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Dispersion relation: c0 =
n l0 = 3 · 108 m/s
cMat = n l0/n(l) |
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Know yout basic equations and
terminology |
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Coherent monochromatic plane wave
E and H perpendicular and in
phase |
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E(r,t)
H(r,t) |
= |
E0
H0 |
·
exp{i(kr –wt)} |
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Reflection always with "angle
in" = "angle out".
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Refraction
is the sudden "bending" or
"flexing" of light beams at the interface |
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Diffraction is the continous "bending" of light beams
around corners; interference effects. |
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Geometric optics
Key paramters |
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Focal length f and
numerical aperture NA of lenses, mirrors. |
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Image formation by simple geometric
constration |
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Various aberrations (spherical. chromatic,
astigmatism, coma, ...) limit performance. |
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Wave optics
Huygens principle: and interference |
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Ultimate limit to resolution |
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Know your basic types of waves: |
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(Running, coherent, monochromatic) plane
wave. |
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Standing
waves = superposition of plane waves. |
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Incoherent, multichromatic real waves |
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Relation s between electrical field
E, magnetic field H and Poynting
vector (energy flow vector) S = E ×
H |
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| [Welect;
magn] |
= |
[Ws
m–3] |
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| E0 |
= |
æ
ç
è |
mrm0
ere0 |
ö
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ø |
½ |
·
H0 |
= |
Zw ·
H0 |
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This equation links energy flow (easy in photon picture) to field strength in wave picture. |
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Zw = wave
impedance of the medium.
Zw(vacuum) = 376,7 W |
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Polarization = key to
"advanced" optics.
Simple case: linear polarization. |
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Plane of polarization contains
E-vector and S
(k) vector. |
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Any (coherent) wave is polarized but net polarization of many waves with random
polarization is zero! |
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Light intensity (µ
E2) between polarizers at angle a scales with (cosa)2. |
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General case: elliptical polarization; important are the two
extremes: linear and circular
polarization. |
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For circular polarizaiton the
E-vector rotates on a circle while moving
"forward". This results from a superposition of two plane waves with
E-vectors ar right angles and a phase difference of p/2. |
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Technically important (3-dim Cinema; Lab
optics) |
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© H. Föll (Advanced Materials B, part 1 - script)
