# How the Direction of Polarization is Related to the Direction of Oscillation in Transverse Waves

Polarization is a property of transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. For example, light waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation. The direction of polarization of a light wave is the direction parallel to the electric field.

## Polarization by Filters

One way to produce polarized light is by passing it through filters, such as certain crystals, that transmit vibration in one plane but not in others. These filters are called polarizers or polarizing filters. A polarizer can block or reduce the intensity of unpolarized light, which consists of waves with random orientations of their electric vectors. A polarizer can also change the orientation of polarized light, depending on the angle between the polarizer’s axis and the direction of polarization.

The intensity of polarized light after passing through a polarizer depends on Malus’s law, which states that:

$$I = I_0 \cos^2 \theta$$

where $I$ is the transmitted intensity, $I_0$ is the incident intensity, and $\theta$ is the angle between the polarizer’s axis and the direction of polarization. According to this law, when $\theta = 0^\circ$, the transmitted intensity is equal to the incident intensity, meaning that no light is blocked by the polarizer. When $\theta = 90^\circ$, the transmitted intensity is zero, meaning that all light is blocked by the polarizer. When $0^\circ < \theta < 90^\circ$, some fraction of light is transmitted and some is blocked by the polarizer.

## Polarization by Reflection

Another way to produce polarized light is by reflection from a surface, such as water or glass. When unpolarized light reflects from a surface, some of its components are preferentially absorbed or transmitted by the surface, resulting in partially or fully polarized reflected light. The degree of polarization depends on the angle of incidence and the material properties of the surface.

There is a special angle of incidence, called Brewster’s angle, at which the reflected light is completely polarized in a plane perpendicular to the plane of incidence. Brewster’s angle can be calculated by:

$$\tan \theta_B = \frac{n_2}{n_1}$$

where $\theta_B$ is Brewster’s angle, $n_1$ is the refractive index of the medium where the light is incident, and $n_2$ is the refractive index of the medium where the light reflects. For example, for air-glass interface, Brewster’s angle is about $56^\circ$, and for air-water interface, it is about $53^\circ$. Polarizing sunglasses use this principle to reduce glare from reflected light by blocking the horizontally polarized component.

## Polarization by Scattering

A third way to produce polarized light is by scattering from particles in a medium, such as air molecules or dust particles. When unpolarized light encounters a particle that is much smaller than its wavelength, some of its components are scattered in different directions with different intensities, resulting in partially or fully polarized scattered light. The degree and direction of polarization depend on the wavelength of light, the size and shape of the particle, and the angle between the incident and scattered rays.

One example of polarization by scattering is the blue color and polarization of the sky. The sunlight that reaches Earth’s atmosphere is mostly unpolarized. However, when it interacts with air molecules, which are much smaller than its wavelength, some of its blue components are scattered more than its red components in all directions. This makes the sky appear blue and polarized in a plane perpendicular to the direction of sunlight. The polarization is maximum at $90^\circ$ from the sun and minimum at $0^\circ$ or $180^\circ$ from

the sun.

## Applications of Polarization

Polarization has many applications in science, technology, and everyday life. Some examples are:

– LCDs (liquid crystal displays) use polarization to control the brightness and contrast of images on screens. LCDs consist of two crossed polarizers with liquid crystals sandwiched between them. By applying electric fields to certain regions of liquid crystals, their orientation can be changed to allow more or less light to pass through.

– 3D glasses use polarization to create stereoscopic effects for movies or games. 3D glasses consist of two lenses with different orientations of polarization. The images projected on a screen are also polarized differently for each eye. By wearing 3D glasses, each eye receives a slightly different image that creates an illusion of depth.

– Polarimetry is a technique that uses polarization to measure the optical activity of substances, such as sugars or proteins. Optical activity is the ability of a substance to rotate the plane of polarization of light that passes through it. By measuring the angle of rotation, the concentration and structure of the substance can be determined.

– Polaroid cameras use polarization to produce instant photographs. Polaroid cameras consist of a lens, a polarizer, and a film that contains layers of chemicals and dyes. When light passes through the polarizer and exposes the film, a chemical reaction occurs that creates an image with different colors depending on the polarization of light.