# The Nature and Propagation of Light

Light and its properties.  Light is an electromagnetic wave.  When emitted or absorbed, it also shows particle properties.  It is emitted by accelerated electric charges.

A wave front is a surface of constant phase; wave fronts move with a speed equal to the propagation speed of the wave.  A ray is a line along the direction of propagation, perpendicular to the wave fronts.

When light is transmitted from one material to another, the frequency of the light is unchanged, but the wavelength and the wave speed can change.  The index of refraction of a material $n=\frac cv$, $\lambda=\frac{\lambda_0}n$.

Reflection and refraction.  $\theta_r=\theta_a$ (law of reflection), $n_a\sin\theta_a=n_b\sin\theta_b$ (law of refraction).

Total internal reflection.  When a ray travels in a material of index of refraction $n_a$ toward a material of index $n_b, total internal reflection occurs at the interface when the angle of incidence equals or exceeds a critical angle $\theta_{\mathrm{crit}}$, $\sin\theta_{\mathrm{crit}}=\frac{n_b}{n_a}$.

Polarization of light.  The direction of polarization of a linearly polarized electromagnetic wave is the direction of the $\vec{E}$ field.

Malus’s law.  When polarized light of intensity $I_{\max}$ is incident on a polarizing filter used as an analyzer, $I=I_{\max}\cos^2\phi$, $I$ is intensity of the light transmitted through the analyzer, $\phi$ is the angle between the polarization direction of the incident light and the polarizing axis of the analyzer.

Polarization by reflection.  When unpolarized light strikes an interface between two materials, Brewster’s law states that the reflected light is completely polarized perpendicular to the plane of incidence (parallel to the interface) if the angle of incidence is $\theta_p=\arctan\frac{n_b}{n_a}$.

Huygens’s principle.  If the position of a wave front at one instant is known, then the position of the front at a later time can be constructed by imagining the front as a source of secondary wavelets.