Polarization of Light — Filters, Malus's Law, Sunglasses
Light polarization explained: transverse waves, polarizing filters, Malus's law I = I₀cos²θ, and why polarized sunglasses kill glare.
Quick answer
Polarization confines light's electric-field vibrations to a single plane. Ordinary light vibrates in all planes; a polarizing filter passes only one plane's vibrations — which is how polarized sunglasses erase glare.
Unit: I in W/m²; θ in degrees
Example: Sunlight reflecting off a lake becomes horizontally polarized. Polarized sunglasses contain a vertical filter that blocks it, cutting the blinding glare while the view stays clear.
What you will learn
- Define polarization as single-plane transverse oscillation
- Explain why only transverse waves polarize
- Apply Malus's law I = I₀cos²θ
- Describe how polarizing filters and sunglasses work
- Give three technological uses of polarization
Light's hidden direction
Light is a transverse wave: its electric field wiggles perpendicular to the direction of travel. But perpendicular to travel is a whole plane of possibilities — up-down, left-right, diagonal. Sunlight uses them all at once: it is unpolarized.
Polarized light wiggles in just one of those directions. Filtering light down to a single vibration plane — and exploiting what passes — is the physics behind sunglasses, LCD screens, and 3D cinema.
The picket-fence filter
A polarizing filter is a molecular picket fence: long aligned molecules absorb electric fields parallel to them and pass perpendicular ones. Hold one up to the sky and rotate it — the brightness shifts as different vibration planes are selected.
Cross two filters at 90° and (nearly) no light passes: the first polarizes vertically, the second passes only horizontal. This simple experiment proves light is transverse — longitudinal waves would sail through regardless of rotation.
Malus’s law
When polarized light meets a filter at angle θ to its polarization direction, the transmitted intensity follows Malus's law:
Crossed polarizers block everything — but slip a third at 45° between them and light reappears. Each filter re-polarizes what it passes, so the middle one creates a component the final filter can transmit. Classical wave logic predicts it exactly.
Malus's law in numbers
Worked example. Polarized light of intensity 100 W/m² meets a filter at 30° to its polarization plane.
Three-quarters passes. At 60° only 25 W/m² survives; at 90°, nothing. Sunglasses exploit exactly this: reflected glare is horizontally polarized, the lens filter is vertical (), and the glare is extinguished while ordinary (mixed) light dims only by half.
Polarization at work
Polarization is everywhere once you look:
- LCD screens sandwich liquid crystals between crossed polarizers; each pixel's crystal twists the polarization by a controlled amount, metering light through.
- Stress analysis engineers view plastic models between polarizers — internal stresses rotate polarization into visible color fringes.
- Bees navigate by the sky's polarization pattern on cloudy days.
- 3D cinemas project left-eye and right-eye images in orthogonal polarizations; cheap glasses decode them.
A property invisible to the naked eye became one of display technology's foundations.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Intensity | W/m² | Transmitted light intensity | |
| Initial intensity | W/m² | Incident polarized intensity | |
| Angle | degrees | Angle between polarization direction and filter axis |
Common mistakes
Polarization selects direction, not brightness — though a filter does absorb the rejected orientations, halving unpolarized light. Perfectly polarized light can be blindingly bright (lasers often are).
Inserting a third polarizer at 45° between crossed ones lets light through! The middle filter re-polarizes at 45°, giving the final filter something to pass. It is a beloved quantum-mechanics demonstration.
Only lenses labeled polarized contain the filtering film. Ordinary tinted lenses just darken everything, glare included.
Real-world applications
Sunglasses: polarized lenses block horizontally-polarized glare reflecting off roads and water.
Photography: polarizing filters deepen skies and cut reflections from glass and water.
LCD screens: liquid crystals rotate polarized light pixel by pixel — your phone screen is a polarization device.
3D movies: theaters project two images with different polarizations; your glasses route each to the correct eye.
Frequently asked questions
What is polarization of light?
Polarization is the restriction of a transverse wave's oscillations to a single plane. Unpolarized light (sunlight, bulbs) vibrates in all planes at once; polarized light vibrates in just one.
What is Malus's law?
I = I₀cos²θ (Malus's law): transmitted intensity equals the incoming intensity times the square of the cosine of the angle between the light's polarization and the filter's axis.
Why can't sound be polarized?
Because only transverse waves have a vibration direction perpendicular to travel that can be filtered. Sound is longitudinal — its oscillations are along the travel direction, so there is nothing to select.
How do polarized sunglasses work?
Reflected glare is strongly polarized horizontally. Polarized sunglasses pass only vertical vibrations, blocking most glare while transmitting ordinary light. Tilt your head 90° and the effect vanishes — a neat test of Malus's law.