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  
Light as electromagnetic wave
Coherent monochromatic plane wave
E and H perpendicular and in phase
 =   E0
    · 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
Imaging with a lens
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
Double slit experiment
Ultimate limit to resolution  
dmin  »  l
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
Wmag   =  m0 · H2
[Welect; magn]   =  [Ws m–3]
E0   =  æ
½  · H0   =  Zw · H0 
<S>  =  E0H0
 =  E02
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)  
Multiple Choice questions to all of 5.1

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