Brewster’s Law Formula

The formula for Brewster’s Law is

μ = tan θ_B

• where μ is the refractive index of the medium
• θ_B is the polarizing angle.

Derivation of Brewster’s Law

Consider the normal to the medium. The sum of angle on one side of the normal will be 180°

Let the incident angle be θ_B

From law of reflection, angle of incidence = angle of reflection = θ_B

According to Brewster’s Law, the reflected and refracted rays are perpendicular to each other. This implies that the angle of incidence i_p and the angle of refraction r_p at Brewster’s angle are complementary.

Now, on one side of normal sum of θ_B, angle of refraction and angle between polarized and unpolarized would be 180°

⇒ θ_B + 90° + r =180°

r = 90° – θ_B

Since Snell’s Law states that μ = sin(i) / sin(r) where, μ is refractive index of medium

Thus,

μ = sin θ_B/ sin(90– θ_B)

μ = sin θ_B/cos θ_B

⇒ μ = tan θ_B

Brewster Law relationship with Snell’s Law

From Snell’s law, the refractive index of the medium is

μ = sin i_p / sin r_p

μ = sin i_p / sin (90-i_p) = sin i_p / cos i_p = tan i_p ∵ (sin (90-a) = cos a)

so, μ = tan i_p = tan θ_B

μ = tan θ_B

Also, according to Snell’s Law describes the relationship between the angles of incidence and refraction for a wavefront traversing across the boundary between two media with different refractive indices is given by:

n₁ sin (i_p) = n₂ sin(r_p)

n₂/n₁ = sin (i_p)/ sin(r_p) = μ

Hence, μ = tan θ_B = n₂/n₁

Brewster’s Law states that when unpolarized light strikes a surface at a specific angle (Brewster angle), the reflected light becomes polarized perpendicular to the plane of incidence. According to Brewster Law of polarization, the refractive index of a medium is equal to the tangent of the polarizing angle. This law finds applications in making polarizing filters for reducing glare in sunglasses and improving image quality in cameras, LCD screens, and optical devices by selectively transmitting polarized light.

In this article we will learn in detail about Brewster Law of Polarization, its formula, derivation, relationship with snell’s law and its application. We will also learn about Brewster angle and its relationship with critical angle in this article.