### 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(krwt)} 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 ö ÷ ø

<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