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Updated on 27th June, 2023 , 4 min read
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:
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.
The Brewster angle formula is:
θB = arctan(n2/n1)
where:
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.
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.
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.
Here are some examples of the application of Brewster's law:
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.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readBrewster’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
Brewster’s law is significant because it allows us to completely polarize light by reflecting it off of a transparent surface. This is useful in a variety of applications, such as polarized sunglasses, liquid crystal displays, and optical tweezers
The two most common applications of Brewster’s law are: Polarized sunglasses: The lenses of polarized sunglasses are made of a material with a specific refractive index that is chosen to match the Brewster angle for water/air. This means that when light is reflected off of a horizontal surface, such as a road or water, the reflected light is polarized in a plane parallel to the surface. The polarized lenses of the sunglasses block this reflected light, which reduces glare. Liquid crystal displays: Liquid crystal displays (LCDs) use Brewster’s law to control the polarization of light. The liquid crystals in an LCD are arranged in a way that they only allow light to pass through when it is polarized in a specific direction. This allows the LCD to display different images by changing the polarization of the light that passes through it.
The formula for Brewster’s law is: tanθB=n2/n1
The refractive index of water is 1.33. So, the Brewster angle for water/air is about 53.13°. This means that if unpolarized light is incident on a water surface at an angle of 53.13°, the reflected light will be completely polarized in a plane perpendicular to the plane of incidence.
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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