What is Brewster’s angle? Derive relation between Brewster angle and refractive index of medium which produces Plane Polarized light.

Brewster's angle, also known as the polarizing angle, is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. This phenomenon occurs when light hits a surface at a specific angle, leading to the production of plane-polarized light.

Understanding Brewster's Angle

The Brewster angle can be defined mathematically using the refractive indices of the two media involved. When unpolarized light strikes the interface between air and a transparent medium (like glass), the angle at which the reflected light is completely polarized is known as Brewster's angle.

Mathematical Derivation

The relationship between Brewster's angle (θ_B) and the refractive index (n) of the medium can be derived from Snell's Law and the concept of polarization. The formula is given by:

• tan(θ_B) = n

Here, θ_B is Brewster's angle, and n is the refractive index of the medium relative to air (which has a refractive index of approximately 1). This equation shows that the tangent of Brewster's angle is equal to the refractive index of the medium.

Practical Implications

When light hits a surface at Brewster's angle, the reflected light is completely polarized perpendicular to the plane of incidence. This property is widely utilized in photography, optics, and various scientific applications to reduce glare and enhance image quality.

In summary, Brewster's angle is crucial for understanding how light interacts with surfaces, particularly in creating polarized light, and is directly related to the refractive index of the medium involved.