AcademyLight Propagation
Academy
Polarization
Level 1 - Physics topic page in Light Propagation.
Principle
Polarization describes the direction of the electric field oscillation in a transverse light wave. Linear polarizers transmit the electric-field component along their transmission axis.
Notation
\(I_0\)
incident intensity
\(\mathrm{W\,m^{-2}}\)
\(I\)
transmitted intensity
\(\mathrm{W\,m^{-2}}\)
\(\theta\)
angle between polarization direction and polarizer axis
\(\mathrm{rad}\)
\(\theta_B\)
Brewster angle
\(\mathrm{rad}\)
\(n_1, n_2\)
refractive indices at an interface
Method
Derivation 1: Use transverse-wave direction
For a light wave traveling in a fixed direction, the electric field oscillates perpendicular to the direction of travel. Linear polarization means the electric field stays in one plane.
Derivation 2: Apply Malus's law
A polarizer passes the field component along its axis. Intensity is proportional to field amplitude squared.
Malus's law
\[I=I_0\cos^2\theta\]
Unpolarized light through one polarizer
\[I=\frac{I_0}{2}\]
Derivation 3: Recognize polarization by reflection
At Brewster's angle, reflected light is strongly plane-polarized.
Brewster angle
\[\tan\theta_B=\frac{n_2}{n_1}\]
Rules
Malus's law
\[I=I_0\cos^2\theta\]
Unpolarized through one polarizer
\[I=\frac{I_0}{2}\]
Brewster angle
\[\tan\theta_B=\frac{n_2}{n_1}\]
Examples
Question
Unpolarized light of intensity
\[100\,\mathrm{W\,m^{-2}}\]
passes through one ideal polarizer. Find the transmitted intensity.Answer
\[I=\frac{I_0}{2}=50\,\mathrm{W\,m^{-2}}\]
Checks
- Polarization is evidence that light is transverse.
- Malus's law applies to already plane-polarized light entering an ideal polarizer.
- Unpolarized light through one ideal polarizer loses half its intensity.
- A second polarizer at \(90^\\circ\) to the first blocks ideal linearly polarized light.