Brewster’s Law – Examples, Definition, Formula, Derivation, FAQ’S

Brewster’s Law in physics describes how the angle of incidence and the angle of polarization of light relate to each other. It establishes that the refractive index of a material determines the angle of incidence at which light becomes perfectly polarized, with the reflected and refracted rays being perpendicular to each other.

What is Brewster’s Law?

Brewster’s Law Formula

The formula for Brewster’s Law relates the Brewster angle (𝜃𝐵​). At which light is perfectly polarized upon reflection, to the refractive indices of the two media involved. It is given by:

where:

• 𝜃𝐵​ is the Brewster angle, at which the reflected light is fully polarized.
• 𝑛₁​ is the refractive index of the initial medium (the medium from which light is coming).
• 𝑛₂ is the refractive index of the second medium (the medium into which light is entering).

At this angle, known as the polarization angle, the reflected light polarizes perpendicular to the plane of incidence.

Brewster’s Law Derivation

Concept: When light hits a material (like glass) at a certain angle, known as the Brewster angle. The reflected light becomes perfectly polarized (vibrates in one direction).

Key Idea: At the Brewster angle, the reflected and refracted light rays are perpendicular to each other.

Snell’s Law: This law relates the angle of incidence and the angle of refraction for light passing from one medium to another: 𝑛₁sin⁡𝜃𝑖=𝑛₂sin⁡𝜃𝑟​

𝑛₁​ and 𝑛₂​ are the refractive indices of the two media (air and glass, for example).

𝜃𝑖​ is the angle of incidence, and 𝜃𝑟​ is the angle of refraction.

Brewster’s Condition: At the Brewster angle, the refracted light’s angle (𝜃𝑟​) and the incident light’s angle (𝜃𝑖=𝜃𝐵​) are related such that: 𝜃𝑟=90⁰−𝜃𝐵​

Simplify the Equation: Substituting 𝜃𝑟=90⁰−𝜃𝐵​ into Snell’s law: 𝑛₁sin⁡𝜃𝐵=𝑛₂cos⁡𝜃𝐵​

Final Formula: Divide both sides by cos⁡𝜃𝐵​: tan⁡𝜃𝐵=𝑛₂𝑛₁

This formula tells us that the Brewster angle (𝜃𝐵​) depends on the refractive indices of the two media involved.

Uses of Brewster’s Law

1. Photography and Filmmaking: Photographers and filmmakers, by using Brewster’s Law, effectively reduce reflections on non-metallic surfaces. With polarizing filters positioned at Brewster’s angle, they consequently enhance image quality, reducing glare from surfaces like water or glass.
2. Optical Devices: Engineers design devices such as lasers and microscopes by using Brewster’s Law. They incorporate Brewster windows to minimize reflection losses and, in turn, improve light transmission.
3. Sunglasses and Eyewear: Manufacturers leverage Brewster’s Law to reduce glare from horizontal surfaces like roads and water, thus improving visual clarity and reducing eye strain.
4. Polarization Studies: Researchers rely on Brewster’s Law to analyze the polarization properties of materials, which is essential in optics and material sciences.
5. Optical Communication: Brewster’s Law optimizes light transmission in fiber optic cables and consequently enhances data transfer efficiency in optical communication systems.
6. Polarimetry: Instruments such as polarimeters apply Brewster’s Law to measure the polarization of light, thereby aiding in various scientific analyses.

Examples for Brewster’s Law

1. Polarized Sunglasses: Sunglasses reduce glare by using Brewster’s Law to cut reflections from surfaces like water or roads.
2. LCD Displays: LCDs employ polarizing filters for brightness and contrast. Brewster’s Law ensures better light transmission for improved image quality.
3. Anti-Reflective Coatings: Optical devices use coatings at Brewster’s angle to reduce glare, boosting light transmission for better efficiency.
4. Photography and Cinematography: Polarizing filters help photographers and filmmakers manage glare and reflections.
5. Fiber Optic Systems: In fiber optics, Brewster’s Law guides design to minimize signal loss from reflections, improving network performance.

FAQ’S

What are Brewsters rules?

Brewster’s Law dictates that reflected light becomes polarized when unpolarized light strikes a transparent medium at Brewster’s angle, where the reflected and refracted rays are perpendicular.

Is Brewster law and Malus law same?

Brewster’s Law deals with polarization by reflection, whereas Malus’s Law quantifies the intensity of polarized light passing through a polarizer, making them fundamentally different.

What is Brewster’s photo for?

Brewster’s photo helps analyze polarization effects, applying Brewster’s Law to observe polarized light reflections for scientific studies, optical designs, and photographic applications.