Brewster’s Law

Brewster’s law tells me the exact angle at which reflected light becomes fully plane-polarised. This happens when light reflects off a surface such as glass, water, or polished stone at a specific angle called the Brewster angle.

At this angle, the reflected light vibrates in only one direction, which is why glare-reducing sunglasses use this idea.

The Brewster angle \(i_B\) is the angle of incidence at which the reflected ray becomes completely polarised. Brewster found that this angle depends only on the refractive index of the medium.

The law is written as:

Here:

• \(i_B\): Brewster angle
• \(\mu\): refractive index of the second medium (usually glass or water)

At the Brewster angle, the reflected and refracted rays are perpendicular to each other. Because of this orientation, the reflected component can only contain vibrations in one direction.

Using the law \( \tan i_B = \mu \), we can find the value of the angle easily.

Glare from water bodies, shiny roads, and car windshields is mostly horizontally polarised. Polarised sunglasses have a vertical transmission axis that blocks this glare. This idea works because such reflected light is naturally polarised near Brewster angle.

Surfaces with distinct refractive indices show clearer Brewster angles. Common examples include:

• Water (\(\mu \approx 1.33\))
• Glass (\(\mu \approx 1.5\))
• Polished plastic
• Quartz

The reflected beam becomes polarised in one direction only. This is possible only for transverse waves, since longitudinal waves cannot be restricted to one vibration direction. The behaviour at Brewster angle is one of the clearest proofs that light is a transverse electromagnetic wave.