- Maxwell’s equation
- Geometrical optics
- Interference
- Diffraction
- Fresnel’s equation
- Group velocity
- Group index
- Quantum mechanical concepts

- Vectors
- Complex numbers
- Partial differentiation
- Fourier transforms

- Wave theory
- Particle theory

- light
- Wave theory: wave => interference, diffraction
- Particle theory: photon

# Wave Nature of Light

## Light Waves in a Homogeneous Medium

### Plane Electromagnetic Wave

- Electric field Ex
- Magnetic field By
- Electromagnetic wave
- traveling wave
- time varying
- perpendicular to each other and the direction of propagation: z
- position z
- time t
- propagation constant, wave number k (2*pi/lambda)
- wavelength lambda
- angular frequency omega
- wave amplitude E0
- Phase constant phi0
- Argument (omega*t – k*z + phi0) => phase phi
- Monochromatic plane wave
- wavefront
- Faraday’s law: time varying magnetic field results in time varying electric fields and vice versa
- optical field

z = a+b\,\mathrm i \\
|z| = \sqrt{a^2 + b^2} \\
z = r \cdot \mathrm{e}^{\mathrm{i}\varphi} = r \cdot (\cos \varphi + \mathrm{i} \cdot \sin \varphi) \\
\phi = \omega t - k z + \phi_0 \\
a^{x+y}=a^x \cdot a^y \\
a^{x\cdot y}=(a^{x})^{y} \\
{\displaystyle a^{-x}={\frac {1}{a^{x}}}=\left({\frac {1}{a}}\right)^{x}} \\
{\displaystyle {\sqrt[{q}]{a^{p}}}=a^{\frac {p}{q}}}