### 5.1.5 Summary to: 5.1 Optics

| Know your numbers and relations for visible light! |  |
For the propagation of light: use the wave model For the generation and disappearance (= absorption) of light: use the photon model
Snellius law: n = sina/sinb with a, b the angle of incidence or propagation, resp.
|  | Wavelengths: l » 400 nm - 800 nm. |
|  | lmat = l0/n. |
|  | Frequency: n» 10 15 Hz. |
|  | Index of refraction: n = er½ » 1,5 - 2,5 |
|  | Energy E » 1,8 eV - 3,2 eV. |
|  | Dispersion relation: c0 = n l0 = 3 · 108 m/s cMat = n l0/n(l) |
| Know yout basic equations and terminology |  |
Coherent monochromatic plane wave E and H perpendicular and in phase
E(r,t) H(r,t) | = | E0 H0 | · exp{i(kr –w t)}
--- | --- | --- | ---
|  | Reflection always with "angle in" = "angle out". |
|  | Refraction is the sudden "bending" or "flexing" of light beams at the interface |
|  | Diffraction is the continous "bending" of light beams around corners; interference effects. |

| Geometric optics Key paramters |  |
|  | Focal length f and numerical aperture NA of lenses, mirrors. |
|  | Image formation by simple geometric constration |
|  | Various aberrations (spherical. chromatic, astigmatism, coma, ...) limit performance. |
| Wave optics Huygens principle: and interference |  |
|  | Ultimate limit to resolution |
dmin | » | l 2NA
--- | --- | ---
| Know your basic types of waves: |
|  | (Running, coherent, monochromatic) plane wave. |
|  | Standing waves = superposition of plane waves. |
|  | Incoherent, multichromatic real waves |

| Relation s between electrical field E, magnetic field H and Poynting vector (energy flow vector) S = E × H |  |
Welect | = | e0 · E2 2
--- | --- | ---
Wmag | = | m0 · H2 2
--- | --- | ---
[Welect; magn] | = | [Ws m–3]
--- | --- | ---
E0 | = | æ ç è | mrm0 ere0 | ö ÷ ø | ½ | · H0 | = | Zw · H0
<S> | = | E0H0 2 | = | E02 Zw
--- | --- | --- | --- | ---
|  | This equation links energy flow (easy in photon picture) to field strength in wave picture. |
|  | Zw = wave impedance of the medium. Zw(vacuum) = 376,7 W |
| Polarization = key to "advanced" optics. Simple case: linear polarization. |  |
|  | Plane of polarization contains E-vector and S (k) vector. |
|  | Any (coherent) wave is polarized but net polarization of many waves with random polarization is zero! |
|  | Light intensity (µ E2) between polarizers at angle a scales with (cosa)2. |
| General case: elliptical polarization; important are the two extremes: linear and circular polarization. |
|  | 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. |
|  | Technically important (3-dim Cinema; Lab optics) |
Questionaire
Multiple Choice questions to all of 5.1

© H. Föll (Advanced Materials B, part 1 - script)