Optical Polarization Equations

By Galen C. Duree, Jr.

Part of Optics For Dummies Cheat Sheet

Optical polarization is the orientation of the planes of oscillation of the electric field vectors for many light waves. Optical polarization is often a major consideration in the construction of many optical systems, so equations for working with polarization come in handy. The following equations highlight some important polarization concepts. The equations listed here allow you to calculate how to make polarized light by reflection and to determine how much light passes through multiple polarizers:

  • Polarizing angle or Brewster’s angle: This angle is the angle of incidence where the reflected light is linearly polarized. Here’s the equation:


  • Malus’ law: This equation allows you to calculate how much polarized light passes through a linear polarizer. The equation for Malus’ law is


  • Phase retardation in a birefringent material: A birefringent material has two indexes of refraction. When you send polarized light into a birefringent material, the two components travel through the material with different speeds. This discrepancy can result in a change in the polarization state or simply rotate the polarization state. Use this equation: