What is meant by polarization of light? Explain polarization by reflection and state Brewster's Law, proving that the reflected and refracted rays are mutually perpendicular when light is incident at the polarizing angle.

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Introduction to Polarization of Light
Ordinary light consists of electric field oscillations in all possible directions perpendicular to the direction of propagation, and such light is called unpolarized light. The phenomenon of restricting the vibrations of light vectors (electric field vector) to a single plane perpendicular to the direction of wave propagation is called polarization of light. This phenomenon conclusively proves the transverse nature of light waves. Polarization by Reflection
When unpolarized light is incident on a transparent medium (such as glass or water) at a specific angle, the reflected light gets partially or completely polarized. This specific angle of incidence is known as the polarizing angle or Brewster's angle (denoted by $ip$). Brewster's Law
Sir David Brewster conducted experiments and discovered a simple relationship between the polarizing angle ($ip$) and the refractive index ($\mu$) of the medium. Brewster's Law states that: The tangent of the polarizing angle of incidence is equal to the refractive index of the medium. 
Mathematically: $$\mu = 	an ip$$ Proof that Reflected and Refracted Rays are Mutually Perpendicular
Let unpolarized light be incident on the surface of a transparent medium of refractive index $\mu$ at the polarizing angle $ip$. According to Snell's law of refraction: $$\mu = \frac{\sin ip}{\sin r}$$ where $r$ is the angle of refraction. According to Brewster's law: $$\mu = 	an ip = \frac{\sin ip}{\cos ip}$$ Comparing both expressions for refractive index $\mu$: $$\frac{\sin ip}{\sin r} = \frac{\sin ip}{\cos ip}$| $$\sin r = \cos ip$$ $$\sin r = \sin(90^\circ - ip)$$ $$r = 90^\circ - ip$$ $$ip + r = 90^\circ$$ Now, let us consider the straight line representing the boundary surface. The sum of angles on one side of the normal is $180^\circ$: $$ip + \angle 	ext{COR} + r = 180^\circ$$ where $\angle 	ext{COR}$ is the angle between the reflected ray and the refracted ray. Substituting $ip + r = 90^\circ$ into the equation: $$90^\circ + \angle 	ext{COR} = 180^\circ$$ $$\angle 	ext{COR} = 180^\circ - 90^\circ = 90^\circ$$ 
Thus, it is proved that the reflected ray and the refracted ray are at right angles ($90^\circ$) to each other when light is incident at the polarizing angle.

CBSE · Class 12 · Physics · Wave OpticsWhat is meant by polarization of light? Explain polarization by reflection and state Brewster's Law, proving that the reflected and refracted rays are mutually perpendicular when light is incident at the polarizing angle.

Polarization by Reflection\nWhen unpolarized light is incident on a transparent medium (such as glass or water) at a specific angle, the reflected light gets partially or completely polarized. This specific angle of incidence is known as the polarizing angle or Brewster's angle (denoted by $i_p$).

Brewster's Law\nSir David Brewster conducted experiments and discovered a simple relationship between the polarizing angle ($i_p$) and the refractive index ($\mu$) of the medium. Brewster's Law states that:

Proof that Reflected and Refracted Rays are Mutually Perpendicular\nLet unpolarized light be incident on the surface of a transparent medium of refractive index $\mu$ at the polarizing angle $i_p$.