Polarization of Light Reference Cheat Sheet

Key Facts

• Light is a transverse electromagnetic wave, so its electric field $\vec{E}$ oscillates perpendicular to its direction of travel.
• The polarization direction of light is defined as the direction of the electric field $\vec{E}$.
• For unpolarized light passing through one ideal polarizer, the transmitted intensity is $I = \frac{I_0}{2}$.
• For polarized light passing through an analyzer, Malus’s law gives $I = I_0 \cos^2 \theta$, where $\theta$ is the angle between the light polarization and analyzer axis.
• Two ideal polarizers crossed at $90^\circ$ transmit no light because $I = I_0 \cos^2 90^\circ = 0$.
• Brewster’s angle satisfies $\tan \theta_B = \frac{n_2}{n_1}$ for light going from medium $1$ into medium $2$.
• At Brewster’s angle, the reflected ray and refracted ray are perpendicular, so $\theta_B + \theta_2 = 90^\circ$.
• Circular and elliptical polarization occur when perpendicular electric field components have phase differences such as $\Delta \phi = \frac{\pi}{2}$.

Vocabulary

Polarization

Polarization is the orientation pattern of the electric field $\vec{E}$ in a transverse light wave.

Polarizer

A polarizer is an optical filter that transmits light whose electric field is aligned with its transmission axis.

Analyzer

An analyzer is a second polarizer used to measure or test the polarization direction of light.

Malus’s Law

Malus’s law states that transmitted intensity through an ideal analyzer is $I = I_0 \cos^2 \theta$.

Brewster’s Angle

Brewster’s angle $\theta_B$ is the angle of incidence where reflected light is maximally plane-polarized and $\tan \theta_B = \frac{n_2}{n_1}$.

Unpolarized Light

Unpolarized light contains electric field oscillations in many random transverse directions.