Question

What is polarization by reflection and Brewster’s law?

Answer 1

Hint: In order to solve this question we will first know what polarization and polarization by reflection means, what is the statement of Brewster’s law and we will derive Brewster's law.

Complete step by step solution:
A wave's polarisation is the direction in which it vibrates (or oscillates). One polarisation is up and down, another is side-to-side, and then there's the diagonal in between.
Polarization by reflection occurs when light is bounced off a reflective or mirrored surface, causing the light to be polarised as it travels away from the surface. When light strikes a surface, some of it will be refracted, bending and passing through the object, while others will be mirrored, bouncing away from it.
Light polarised in the direction of reflection, in the same plane as the incident and reflected rays, is more likely to be refracted, whereas light polarised at 90 degrees to this plane is more likely to be reflected. This means the polarised light is light that bounces off surfaces and reaches your eyes.
We know from Ray optics that when a light is incident on the surface of a transparent medium with a refractive index of ($\mu $), some light is reflected and some is refracted; we also know from Snell's law that as the incident angle increases, the angle of refraction increases; and we know from the law of reflection that as the incident angle increases, the angle of refraction increases as well.
Angle of incidence is equivalent to angle of reflection
When angle of incident, ${{\theta }_{i}}={{\theta }_{p}}$
When the reflected and refracted rays are perpendicular to each other, the reflected light is fully plane polarised, and this angle (${{\theta }_{p}}$) is referred to as the angle of polarisation.
Brewster’s Law statement is given as:
The reflected and refracted rays would be perpendicular to each other when the incident angle equals the polarisation angle.
From Snell’s law
$\mu =\dfrac{\sin i}{\sin r}=\dfrac{\sin {{\theta }_{p}}}{\sin {{\theta }_{r}}}$
Where, $\mu $ is the refractive index of the medium,
${{\theta }_{i}}$ is the angle of incidence and
${{\theta }_{p}}$ is the angle of polarization.
Since reflected ray perpendicular to refracted ray $90{}^\circ +{{a}_{p}}+{{a}_{r}}=180{}^\circ $
Therefore, ${{\theta }_{r}}=90{}^\circ -{{\theta }_{p}}$. So, $\mu =\dfrac{\sin {{\theta }_{p}}}{\sin \left( 90{}^\circ -{{\theta }_{p}} \right)}=\dfrac{\sin {{\theta }_{p}}}{\cos {{\theta }_{p}}}=\tan {{\theta }_{p}}$ is known as Brewster’s Law.

Note:
Polarized sunglasses are a popular example of Brewster's law in action. Brewster's angle is used in the design of these glasses. Polarized glasses minimize glare reflected directly from the sun as well as from horizontal surfaces such as the road and water.