Polarization of Light

Sunglasses that know which way is up

On a bright winter day the glare off snow, wet roads and lakes can be blinding. Polarized sunglasses cut that glare dramatically, while ordinary tinted lenses only dim everything. Tilt your head 90° while wearing them and the glare comes back. These lenses work because light is a transverse wave whose vibrations have a direction, and that direction can be filtered.

What polarization is

In a transverse wave the vibrations are perpendicular to the direction of travel. A rope wave travelling east can vibrate up and down, side to side, or at any angle in between. If you pass the rope through a fence with vertical slots, only up-and-down vibrations get through. The wave on the far side is polarized: it vibrates in one direction only.

Light is a transverse electromagnetic wave: its electric field vibrates perpendicular to the direction of travel. In light from the Sun or a bulb, the vibration direction changes randomly and rapidly, so all directions are present: this is unpolarized light.

A longitudinal wave such as sound vibrates along its direction of travel, so there is no sideways direction to filter: longitudinal waves cannot be polarized. The fact that light can be polarized is strong evidence that it is a transverse wave.

Polarizing filters and Malus's law

A polarizing filter (polarizer) contains long molecules lined up in one direction. It transmits the component of the electric field along its transmission axis and absorbs the rest.

• Unpolarized light through one ideal polarizer: half the intensity is transmitted, I = I₀/2, and the light leaving is polarized along the axis.
• Polarized light of intensity I₀ through a polarizer whose axis makes angle θ with the light's vibration direction: only the field component E cos θ passes, and intensity depends on the square of the field, so

I = I₀ cos² θ (Malus's law)

• At θ = 0°, all the light passes. At θ = 90° (crossed polarizers), none passes.

Polarization by reflection and by scattering

Reflection. When unpolarized light reflects from a non-metallic surface such as water, snow, glass or a road, the reflected light is partly polarized parallel to the surface (horizontally, for a lake or a road). At one special angle of incidence, Brewster's angle, the reflected light is completely polarized. This happens when the reflected and refracted rays are at 90° to each other, which gives

tan θ_B = n₂ / n₁

For light in air reflecting from water, θ_B = tan⁻¹(1.33) = 53°.

Polarized sunglasses have their transmission axis vertical. They absorb much of the horizontally polarized glare from horizontal surfaces while letting through vertically vibrating light from the rest of the scene. Photographers use polarizing filters on cameras for the same reason, and to see into water or through shop windows.

Scattering. Sunlight scattered by air molecules is partly polarized, most strongly in directions about 90° away from the Sun. Look at the blue sky through polarized sunglasses and rotate them: part of the sky darkens and brightens. (Never look at the Sun itself.)

Colours from stress, and screens

Photoelasticity. Clear plastics such as rulers, protractors, plastic cutlery or packing tape become slightly different for different vibration directions when they are stretched or stressed. Between crossed polarizers, they change the polarization of each wavelength by a different amount, so some colours get through the second polarizer and others are blocked. The result is bands of colour that map the stress: crowded fringes show where stress is high. Engineers have used plastic models viewed this way to find weak spots in designs such as hooks, gears and bridges. This is another way to separate white light into colours (expectation E3.3).

LCD screens. A liquid-crystal display places liquid crystals between two polarizers. An electric field changes how the liquid crystal rotates the light's polarization in each tiny pixel, so the second polarizer passes more or less light. That is why an LCD screen's light is polarized, and why it can look dark through polarized sunglasses at some angles.

3D movies often use glasses that send differently polarized images to each eye.