Brewster's Law

Brewster's law is the tangent of the angle of incidence for which a refracted ray is completely polarized is equal to the refractive index of the medium. The angle of incidence at which this occurs is called the Brewster angle.In other words, when a beam of unpolarized light is incident on a transparent surface at the Brewster angle, the reflected light is completely polarized in a direction perpendicular to the plane of incidence. The refracted light is also polarized but in the plane of incidence.

μ = tan ip

where:

• μ refers to the refractive index of transparent medium
• ip is the polarizing angle of incidence or a Brewster angle

The refractive index of glass is 1.5, so the Brewster angle for glass/air is about 56°. This means that if a beam of unpolarized light is incident on a glass surface at an angle of 56°, the reflected light will be completely polarized in a direction perpendicular to the plane of incidence.

Brewster's law has many applications in optics, including constructing polarizing filters and sunglasses. It is also used in the study of reflection and refraction of light.

Brewster's law can be explained by the wave nature of light. When unpolarized light is incident on a transparent surface, the electric field of the light wave is oscillating in all directions perpendicular to the direction of propagation. However, at the Brewster angle, the electric field of the reflected light is oscillating parallel to the surface. This is because the component of the electric field that is perpendicular to the surface is completely refracted into the transparent surface.

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Brewster's Law: Brewster Angle Formula

The Brewster angle formula is:

θB = arctan(n2/n1)

where:

• θB is the Brewster angle
• n1 is the refractive index of the first medium (the medium from which the light is incident)
• n2 is the refractive index of the second medium (the medium into which the light is refracted)

For example, if the light is incident from the air (n1 = 1) onto a glass surface (n2 = 1.5), then the Brewster angle is arctan(1.5/1) = 56.3 degrees.

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Brewster's Law: Brewster Law Derivation

The Brewster angle formula can be derived from Snell's law of refraction. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.

When unpolarized light is incident at the Brewster angle, the reflected light is completely polarized in the plane perpendicular to the plane of incidence. This is because the component of the electric field of the light wave that is parallel to the surface is completely refracted into the second medium.

The Brewster angle formula is a useful tool for understanding the polarization of light and its applications. It is used in a variety of applications, including polarizing sunglasses, liquid crystal displays, and optical tweezers.

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Brewster's Law: Brewster Law of Polarization

Brewster's law is a relationship between the angle of incidence of unpolarized light on a transparent surface and the angle of refraction of the reflected light. It states that the tangent of the angle of incidence, called the polarizing angle, is equal to the refractive index of the transparent surface.

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Brewster's Law: Application Of Brewster's Law

Here are some examples of the application of Brewster's law:

• Polarizing sunglasses: Polarizing sunglasses work by using a special filter that reflects light that is polarized in a particular direction. The filter is aligned at the Brewster angle for the wavelength of light that it is designed to block. This means that only light that is polarized perpendicular to the filter is transmitted, while light that is polarized parallel to the filter is reflected.

• Liquid crystal displays (LCDs): LCDs use a special material called liquid crystal to control the polarization of light. The liquid crystal molecules can be aligned in a particular direction, which determines the polarization of the light that is transmitted through them. By controlling the alignment of the liquid crystal molecules, it is possible to create LCDs that can display different images.

• Optical tweezers: Optical tweezers are a type of micromanipulation technique that uses a laser beam to trap and manipulate small particles. The laser beam is focused on a small spot, and the light that is reflected from the particle is polarized. The polarization of the reflected light depends on the angle of incidence, and at the Brewster angle, the reflected light is completely polarized. This allows the particle to be trapped and manipulated by the laser beam.

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Brewster's Law: Solved Example

Let's solve an example to understand Brewster's Law better:

Example: A beam of light is incident from air (refractive index n1 = 1) onto a glass surface (refractive index n2 = 1.5). Find the Brewster's angle for this system.

Solution: We have the following values: n1 = 1 (refractive index of air) n2 = 1.5 (refractive index of glass)

Using the formula: tan(θ_B) = n2 / n1

Substituting the given values: tan(θ_B) = 1.5 / 1 tan(θ_B) = 1.5

To find the Brewster's angle, we need to take the inverse tangent (arctan) of both sides:

θ_B = arctan(1.5)

Using a calculator, we find: θ_B ≈ 56.31 degrees

Therefore, the Brewster's angle for the system is approximately 56.31 degrees.

At this angle, the reflected light will be completely polarized, with its electric field oscillating perpendicular to the surface of the glass.