Brewster’s law is one of those concepts of physics that often come up in informal conversation, but it is not easy to define. In a recent study, researchers from the University of Pennsylvania provided clarity on the concept and demonstrated how it could be used to improve the performance of lasers. Here, we look at Brewster’s Law and what these new findings could mean for future research and applications.

Brewster’s Law states that when light falls on a surface at a particular angle, the more reflected light will travel in the direction perpendicular to the surface than in any other direction.

Brewster’s law definition

According to this law, when unpolarised light is incident at polarising angle ip  on an interface separating air from a transparent medium of refractive index (n), then reflected light is fully polarised in a direction perpendicular to the plane of incidence provided. 

n = tan ip 

This relation is called Brewster’s law.

Brewster angle

The Brewster angle is demonstrated as the angle at which light waves reflect off of a surface such that there is no phase difference between the reflected and incident waves. This angle is dependent on the refractive index of the given material and the wavelength of the light. For a given material, the Brewster angle increases as the wavelength of the light decreases.

The Brewster angle is different for different materials. For example, the Brewster angle for water is 54 degrees, while the Brewster angle for glass is 56 degrees. When light reflects off a surface at the Brewster angle, all reflected light will be polarised.

Difference between Brewster angle and critical angle

The critical angle is demonstrated as the angle at which light waves are internally reflected off of a surface. This angle is also dependent on the refractive index of the given material and the wavelength of the light. For a given material, the critical angle decreases as the wavelength of the light decreases. Let’s understand the difference between the critical angle and the Brewster angle.

• The difference between the Brewster angle and the critical angle is the Phase Difference Angle (PDA). The PDA measures how much phase shift occurs when light waves reflect off a surface at a critical angle. The PDA is dependent on the refractive index of the material and the wavelength of the light. For a given material, the PDA decreases as the wavelength of the light decreases.

• The Brewster angle is always smaller than the critical angle. The Brewster angle accounts for reflection and refraction, while the critical angle only accounts for reflection. There is no phase shift between the reflected and incident waves when light waves come out from a surface at the Brewster angle. However, when light waves come out at a surface at the critical angle, there is a phase shift of 180 degrees between the reflected and incident waves.

• The Brewster angle is named after Sir David Brewster, who discovered it in 1815. The critical angle is named after Christiaan Huygens, who first described it in 1690.

Brewster law derivation

Let’s understand the Brewster law derivation. 

Let’s consider, an unpolarized light is incident along with path AP at brewster’s angle  ‘ip  ’ on the interface XY separating air from a medium of refractive index ‘n’. The light reflected along PB is completely plane polarised. The refracted along pc is completely plane polarised. The light refracted along the pc continues to be unpolarised.

Thus according to Brewster.

∠ BPY + ∠  YPC = 900

or

(90 – ip ) + (90 – r) = 90

Where,

R is the angle of refraction

or

R = 90 – ip 

According to snell’s law

n = sin isin r

Where i = ip  and r = 90 – ip 

n = sin isin(90 – r) = sin ipcos ip = tan ip

n = tan ip

Brewster law of polarisation

The Brewster law of polarisation states that when light is incident on a surface at the Brewster angle, the reflected light will be polarised at 90° or perpendicular to the incident light. The Brewster angle is determined by the refractive index of the given material and the wavelength of the light.

The phenomenon is explained by considering the wave nature of light. When light waves are incident on a surface, they are partly reflected and partly transmitted. The reflected waves interfere with each other, and this interference is what produces polarised light.

This phenomenon has many practical applications. For example, it is used in polarising filters for cameras and sunglasses. It is also used in liquid crystal displays (LCDs), where the Brewster angle is used to control the polarisation of the light passing through the LCD.

Limitations of Brewster’s Law

Brewster’s Law is only valid for materials with a refractive index greater than 1.5. Additionally, the angle of incidence must be less than 90 degrees. The reflected light will not be completely polarised for materials with a refractive index of less than 1.5.

Conclusion

Brewster’s Law is a fascinating optical principle that states when light hits a surface at an angle, the reflected light will be in phase with the incoming light. If one understands how this law works and its applications, they can apply it to their design. One can also create interfaces and graphics that are more visually pleasing and easier to read. This Law is named after the scientist Sir David Brewster. He first discovered it in 1815. The refractive index of the material determines it. Brewster’s law is used in many fields, including optics, engineering, and manufacturing.