Light is an electromagnetic wave, and its electric field can vibrate in different directions perpendicular to the direction of travel. Polarization describes the pattern of these vibrations, such as random directions in unpolarized light or one fixed direction in linearly polarized light. This matters because polarizing filters can control light intensity, reduce glare, and reveal wave behavior that ordinary brightness measurements cannot show.
Polarization is used in sunglasses, camera filters, LCD screens, 3D movies, and stress analysis of transparent materials.
A polarizing filter has a transmission axis that allows the electric field component parallel to that axis to pass while absorbing or blocking the perpendicular component. Unpolarized light passing through one ideal polarizer emerges linearly polarized with half its original intensity. When polarized light reaches a second polarizer, the transmitted intensity depends on the angle between their axes according to Malus's law.
Crossed polarizers at 90 degrees ideally block all light, while intermediate angles allow partial transmission.
Key Facts
- Light is a transverse electromagnetic wave, so its electric field oscillates perpendicular to its direction of travel.
- Unpolarized light has electric field vibrations in many random transverse directions.
- An ideal polarizer transmits the electric field component parallel to its transmission axis.
- Unpolarized light through one ideal polarizer has intensity I = I0/2.
- Malus's law for polarized light is I = I0 cos^2(theta), where theta is the angle between polarizer axes.
- Crossed polarizers have theta = 90 degrees, so I = I0 cos^2(90 degrees) = 0 for ideal filters.
Vocabulary
- Polarization
- Polarization is the orientation pattern of the electric field vibrations in a transverse wave such as light.
- Unpolarized light
- Unpolarized light is light whose electric field vibrates in many random directions perpendicular to its direction of travel.
- Linearly polarized light
- Linearly polarized light is light whose electric field vibrates along one fixed direction.
- Transmission axis
- The transmission axis of a polarizer is the direction of electric field vibration that the filter allows to pass.
- Malus's law
- Malus's law states that the intensity transmitted through an analyzer is I = I0 cos^2(theta) for incident linearly polarized light.
Common Mistakes to Avoid
- Using I = I0 cos(theta) instead of I = I0 cos^2(theta). Intensity depends on the square of the electric field amplitude, so the cosine must be squared.
- Applying Malus's law directly to unpolarized light without the first-polarizer factor. Unpolarized light first loses half its intensity through an ideal polarizer before angle effects are considered.
- Thinking a polarizer blocks light traveling in one direction. A polarizer affects the direction of electric field vibration, not the left to right path of the beam.
- Assuming parallel and perpendicular filter axes give the same result. Parallel axes transmit maximum light after the first polarizer, while perpendicular crossed axes ideally transmit zero light.
Practice Questions
- 1 Unpolarized light with intensity 800 W/m^2 passes through one ideal polarizer. What is the transmitted intensity?
- 2 Linearly polarized light of intensity 120 W/m^2 passes through a polarizing filter whose axis is 30 degrees from the light's polarization direction. Use I = I0 cos^2(theta) to find the transmitted intensity.
- 3 Explain why polarized sunglasses reduce glare from a horizontal road or water surface while still allowing some other light to reach your eyes.