Polarization

Put on polarized sunglasses and look at the glare on a lake. Tilt your head 90°. The glare either appears or disappears depending on the angle. The glasses aren’t just darkening everything — they’re selectively blocking light waves that oscillate one way while letting through waves that oscillate another way.

That selective filtering is polarization. It only works because light is a transverse wave. Sound (longitudinal) can’t be polarized — there’s nothing to align. Polarization is one of the strongest pieces of evidence that light is transverse, and it’s behind sunglasses, LCD screens, photographer’s polarizers, and 3D movie glasses.

Unpolarized vs. Polarized Light

In an unpolarized light beam, the electric field oscillates in all directions perpendicular to the direction of travel. Sunlight, incandescent bulbs, fluorescent bulbs — most natural light is unpolarized. The field vectors point in random directions and change rapidly.

In a linearly polarized beam, the electric field oscillates in only one plane. All field vectors aligned in the same direction.

Polarizers

A polarizing filter transmits only the component of light oscillating along its transmission axis. Everything else gets absorbed.

What happens when unpolarized light hits a polarizer? Exactly half the intensity passes through, and the transmitted light is now linearly polarized along the filter’s axis.

Malus’s Law

When already-polarized light hits a second polarizer (called the analyzer), the transmitted intensity depends on the angle between the polarization direction and the analyzer’s transmission axis:

Key cases to memorize:

• $\theta = 0°$: $\cos^2 0 = 1$ → all polarized light passes (axes aligned).
• $\theta = 30°$: $\cos^2 30° = 3/4$ → 75% passes.
• $\theta = 45°$: $\cos^2 45° = 1/2$ → 50% passes.
• $\theta = 60°$: $\cos^2 60° = 1/4$ → 25% passes.
• $\theta = 90°$: $\cos^2 90° = 0$ → nothing passes (“crossed polarizers”).

Multiple Polarizers — The Three-Polarizer Trick

A classic MCAT problem: two crossed polarizers block all light. But inserting a third polarizer at 45° between them suddenly allows some light through. How does adding more filters let more light through?

1. Unpolarized light hits Polarizer 1 (vertical). Intensity drops to $I_0/2$. Light is now vertically polarized.
2. Vertically polarized light hits Polarizer 2 (at 45° from vertical). Malus: $I = (I_0/2)\cos^2 45° = I_0/4$. Light is now polarized at 45°.
3. Light polarized at 45° hits Polarizer 3 (horizontal — that’s 45° from the previous polarization). $I = (I_0/4)\cos^2 45° = I_0/8$.

Without the middle polarizer, P1 and P3 are 90° apart and block everything. Inserting the 45° polarizer in the middle rotates the polarization direction partway, which lets some light squeeze through the final filter.

Polarization by Reflection (Brewster’s Angle)

Light can become partially polarized when it reflects off a surface. At a specific angle called Brewster’s angle, the reflected light is completely polarized (in the horizontal plane, for a horizontal surface like a road or lake).

This is why glare off a lake or wet road is partially polarized — and why polarized sunglasses (oriented to block horizontally polarized light) reduce glare so dramatically. The same principle is used in photography: a polarizing filter on a camera lens cuts reflections off water, glass, and shiny surfaces, letting you photograph through windows or into lakes.

Circular Polarization