Unit 13: Polarization

1. The Phenomenon of Polarization

Polarization is a fundamental property of light that describes the orientation of the oscillations of its electric field vector. In simpler terms, it refers to the restriction of light vibrations to a single plane. This phenomenon is a direct consequence of light being a transverse wave.

What are Transverse Waves?

A transverse wave is a wave in which the particles of the medium oscillate perpendicular to the direction of energy transfer. Light, being an electromagnetic wave, consists of oscillating electric and magnetic fields that are perpendicular to each other and also perpendicular to the direction in which the light wave is propagating. This perpendicular relationship is crucial for polarization.

Unpolarized Light

Most natural light sources, such as the sun or a typical incandescent bulb, emit unpolarized light. Unpolarized light is characterized by vibrations occurring in all possible planes perpendicular to the direction of propagation. Imagine looking at a beam of unpolarized light head-on; the electric field vectors would be vibrating in every direction around the central axis of the beam.

Definition: Unpolarized light consists of electromagnetic waves where the electric field vectors vibrate in all planes perpendicular to the direction of propagation.

Polarized Light

When light is polarized, its vibrations are restricted to a single plane. This plane is often referred to as the plane of polarization. If we were to observe a beam of polarized light head-on, all the electric field vectors would be vibrating along a single line or within a single plane.

Definition: Polarized light consists of electromagnetic waves where the electric field vectors vibrate in a single plane perpendicular to the direction of propagation.

Why Only Transverse Waves Can Be Polarized?

Longitudinal waves, such as sound waves, are waves in which the particles of the medium oscillate parallel to the direction of energy transfer. Because the oscillations are already confined to a single direction (parallel to propagation), there is no additional plane to restrict them to. Therefore, longitudinal waves cannot be polarized.

Light, being a transverse wave, has oscillations that can occur in any plane perpendicular to its direction of travel. This inherent freedom of oscillation in multiple planes allows for the restriction of these vibrations to a single plane, a process we call polarization.

Methods of Producing Polarized Light

There are several ways to produce polarized light from unpolarized light:

Polarization by Reflection: When unpolarized light reflects off a non-metallic surface, the reflected light can become partially or completely polarized.
Polarization by Scattering: Light scattered by small particles, such as molecules in the atmosphere, can become polarized.
Polarization by Absorption (Dichroism): Certain materials, known as dichroic materials, selectively absorb light vibrating in certain planes while allowing light vibrating in other planes to pass through. This is the principle behind polaroid filters.
Polarization by Birefringence: Some crystalline materials exhibit different refractive indices for light polarized in different directions, leading to the separation of polarized components.

2. Brewster's Law and the Transverse Nature of Light

Brewster's Law provides a quantitative relationship between the angle of incidence, the refractive indices of two media, and the polarization of reflected light. It is a crucial piece of evidence supporting the transverse nature of light.

Brewster's Angle

When unpolarized light is incident on the interface between two transparent dielectric media, the reflected light is generally partially polarized. However, at a specific angle of incidence, known as Brewster's angle (or the polarizing angle), the reflected light is completely polarized.

At Brewster's angle, the reflected light is polarized perpendicular to the plane of incidence, and the refracted light is partially polarized in the plane of incidence. Furthermore, at this angle, the reflected ray and the refracted ray are perpendicular to each other.

Brewster's Law

Brewster's Law states that the tangent of the polarizing angle is equal to the ratio of the refractive index of the second medium to the refractive index of the first medium.

The formula for Brewster's Law is:

tan θ_p = n₂ / n₁

Where:

θ_p is the polarizing angle (Brewster's angle).
n₁ is the refractive index of the first medium (where the light is incident from).
n₂ is the refractive index of the second medium (where the light is transmitted into).

Confirmation of Transverse Nature

Brewster's Law provides strong evidence for the transverse nature of light. Let's consider the situation at Brewster's angle:

The incident light is unpolarized.
The reflected light is completely polarized perpendicular to the plane of incidence.
The refracted light is partially polarized in the plane of incidence.
Crucially, the reflected ray and the refracted ray are perpendicular to each other.

Consider the oscillations of the electric field vector. If light were a longitudinal wave, the oscillations would be along the direction of propagation. When a longitudinal wave reflects, the reflected wave would also be longitudinal, and its oscillations would be along the direction of the reflected ray. Similarly, the refracted wave would be longitudinal, with oscillations along the direction of the refracted ray. If the reflected and refracted rays are perpendicular, it would be impossible for the oscillations to be along both directions simultaneously.

However, for a transverse wave, the electric field oscillations are perpendicular to the direction of propagation. At Brewster's angle, the reflected ray and the refracted ray are perpendicular. If the reflected light is polarized perpendicular to the plane of incidence, its electric field oscillations are in a direction perpendicular to both the incident and reflected rays. For the refracted light, its oscillations are in the plane of incidence. The condition that the reflected and refracted rays are perpendicular means that the oscillations of the electric field in the reflected ray are in a direction that is perpendicular to the oscillations of the electric field in the refracted ray. This is consistent with the transverse nature of light and the vector nature of its electric field oscillations.

Example:

Suppose unpolarized light is incident from air (n₁ ≈ 1.00) onto water (n₂ ≈ 1.33). Let's calculate the Brewster's angle:

tan θ_p = n₂ / n₁ = 1.33 / 1.00 = 1.33

θ_p = arctan(1.33) ≈ 53.1°

At an angle of incidence of approximately 53.1°, the light reflected from the surface of the water will be completely polarized perpendicular to the plane of incidence.

Applications related to Brewster's Angle

Reducing Glare: Polarized sunglasses are designed to block horizontally polarized light, which is the type of light that is strongly reflected from horizontal surfaces like roads and water bodies (glare). By filtering out this glare, they improve visibility and reduce eye strain.
Optical Instruments: Brewster windows are used in lasers and other optical systems. They are angled surfaces that allow light to enter or exit without reflection, thereby minimizing light loss and preventing unwanted back-reflections.

3. Polaroid: The Polarizing Filter

A polaroid is a type of polarizing filter that can produce polarized light from unpolarized light. It utilizes a phenomenon called dichroism.

Dichroism and Polaroid Filters

Dichroism is the property of certain materials that absorb light waves vibrating in one direction more strongly than light waves vibrating in a direction perpendicular to it. Polaroid filters are made of long-chain polymer molecules that are aligned in a particular direction. These molecules preferentially absorb light whose electric field vector vibrates parallel to the direction of molecular alignment.

When unpolarized light passes through a polaroid filter:

The light vibrating parallel to the direction of the aligned molecules is absorbed.
The light vibrating perpendicular to the direction of the aligned molecules is transmitted.

The result is that the transmitted light is plane-polarized, with its electric field vector vibrating in a plane perpendicular to the direction of the molecular alignment in the polaroid. The direction perpendicular to the direction of molecular alignment is called the transmission axis of the polaroid.

Transmission Axis

The transmission axis of a polaroid filter is the direction along which the electric field of the transmitted light is oriented. If polarized light with its electric field vibrating at an angle θ with respect to the transmission axis of a polaroid encounters the polaroid, the intensity of the transmitted light is given by Malus's Law:

I = I₀ cos² θ

Where:

I is the intensity of the transmitted light.
I₀ is the initial intensity of the polarized light incident on the polaroid.
θ is the angle between the plane of polarization of the incident light and the transmission axis of the polaroid.

Crossed Polaroids

When two polaroid filters are placed one after another, and their transmission axes are perpendicular to each other, they are said to be "crossed."

If unpolarized light passes through the first polaroid (polarizer), it becomes plane-polarized. Let the transmission axis of the first polaroid be along the vertical direction. The transmitted light will have its electric field oscillating vertically.

Now, if this polarized light encounters a second polaroid (analyzer) whose transmission axis is perpendicular to the first (i.e., horizontal), the angle θ between the plane of polarization of the incident light (vertical) and the transmission axis of the second polaroid (horizontal) is 90°. According to Malus's Law:

I = I₀ cos²(90°) = I₀ * 0² = 0

Therefore, when two polaroids are crossed, they block all light.

Example:

Unpolarized light with intensity I_unpolarized passes through a polaroid (polarizer) with transmission axis along the vertical direction. The intensity of the polarized light after the first polaroid is I₀ = I_unpolarized / 2, and it is vertically polarized.

This vertically polarized light then passes through a second polaroid (analyzer) whose transmission axis is horizontal. The angle between the vertical polarization and the horizontal transmission axis is 90°.

The intensity of light transmitted through the second polaroid is:

I = I₀ cos²(90°) = (I_unpolarized / 2) * 0² = 0

Thus, no light is transmitted through the crossed polaroids.

Applications of Polaroid Filters

Polaroid filters have a wide range of practical applications:

Polarized Sunglasses: As mentioned earlier, these sunglasses reduce glare by filtering out horizontally polarized light reflected from surfaces.
LCD Screens (Liquid Crystal Displays): LCD technology relies heavily on polarization. Liquid crystals can rotate the plane of polarization of light. By using polarizers and controlling the orientation of the liquid crystals with an electric field, specific pixels can be made to block or transmit light, forming images.
3D Movies: Two images, one for each eye, are projected with different polarization orientations (e.g., one vertically polarized, the other horizontally polarized, or using circular polarization). Special glasses with corresponding polarizing lenses allow each eye to see only its intended image, creating the illusion of depth.
Photography: Polarizing filters can be used in cameras to reduce reflections from non-metallic surfaces (like water or glass) and to enhance the saturation of colors, especially the blue of the sky.
Microscopy: Polarized light microscopy is used to study the optical properties of materials, particularly crystalline structures, which often exhibit birefringence.
Stress Analysis: When transparent materials are subjected to stress, they can become birefringent. Viewing these materials between crossed polaroids reveals stress patterns as colored fringes, allowing engineers to analyze stress distribution.

In summary, polarization is a key characteristic of transverse waves like light, allowing us to manipulate its properties for a multitude of technological advancements. From reducing glare to creating immersive 3D experiences, the principles of polarization and tools like polaroids are fundamental to modern optics and display technologies.