# 9.4.2 Polarization

Imagine an attempt to transmit a rope wave through a vertical slit. If the rope is oscillating vertically, then the wave would travel unimpeded through the slit. On the other hand, if the rope is vibrating horizontally, then the wave would be totally absorbed by the slit. Welcome to the magical world of polarization.

It is useful to note that polarization is a phenomenon unique to transverse waves. It is not applicable to longitudinal waves (since they can only vibrate in one direction). In fact, the fact that light can be polarized is evidence that light is a transverse wave.

Passing Unpolarized Light through a Polarizer

Light is a transverse wave. If a light wave is propagating along the z-axis, then its E-field could be oscillating in the x-axis, or y-axis, or any direction in the xy plane. It turns out that light waves emitted by most light sources are unpolarized light, which is to say the light beam contains a mixture of waves with E-field oscillating in all possible directions in the xy plane. (Mathematically, we can model natural light as two arbitrary, incoherent, perpendicularly polarized waves of equal amplitude.)

There are materials such as Polaroids which, due to their chemical structure, absorb only electric fields oscillating in the direction of their polymer chains. Electric fields oscillating in the direction perpendicular to the polymer chains are not absorbed. The Polaroid is an example of a polarizer, and the direction of the polymer chains is called the polarization direction.

When a beam of unpolarized light passes through a polarizer, it becomes polarized. After polarization, the oscillation of electric field will only be in the polarization direction of the polarizer (because the electric field oscillating in the perpendicular direction has been absorbed).

Passing Polarized Light through a Polarizer

The fun part begins now. Suppose we pass a beam of polarized light with amplitude A0 and intensity I0 through a second polarizer.

If the 2nd polarizer’s polarization direction is parallel to the 1st polarizer’s, then we get 100% transmission. On the other hand, if the two polarizers’ polarization directions are perpendicular to each other, then we get 0% transmission.

Now, what happens if they are neither parallel nor perpendicular, but misaligned by some angle θ? Easy. We can always resolve the amplitude of the electric field A0 (of the polarized light) into the components parallel and perpendicular to the polarization direction (of the polarizer), A0cosθ and A0sinθ.

The parallel component will be completely passed through, while the perpendicular component will be completely absorbed. In other words,

$\displaystyle \displaystyle A={{A}_{0}}\cos \theta$

Since $\displaystyle \displaystyle \mathrm{I}\propto {{A}^{2}}$, we arrive at Malu’s Law

$\displaystyle \displaystyle \mathrm{I}={{\mathrm{I}}_{0}}{{\cos }^{2}}\theta$

Video Explanation

What is Polarization

Demonstration

Polarizers

Polarized Light Around Us

LCD Projectors

Newton or Einstein?

Polarization by Reflection

Concept Test

1833

Animation

Cabrillo Applet