Final answer:
By applying Brewster's Law and the law of reflection, we can prove that at the polarizing angle, known as Brewster's angle, the reflected and refracted rays are at right angles to each other. Using the mathematical expression for Brewster's Law and geometrical reasoning based on the sum of angles in a triangle, this principle is confirmed.
Step-by-step explanation:
To show that when light is incident on a transparent substance at the polarizing angle, the reflected and refracted rays are at right angles to each other, we need to apply the concept of Brewster's Law. According to Brewster's Law, when light is incident at a certain angle, known as Brewster's angle, the reflected light is completely polarized. This law is mathematically expressed as tan θ = ℓ/ℓi, where θ is the Brewster's angle, ℓ is the refractive index of the transparent substance, and ℓi is the refractive index of the medium in which the incident and reflected light is present, typically air.
The law of reflection states that the angle of incidence is equal to the angle of reflection. When a ray of light hits the surface at Brewster's angle, the angle between the reflected ray and the refracted ray is 90 degrees. This can be proven geometrically: let the angle of incidence be θ, making the angle of reflection also θ. The refracted ray makes an angle of 90 - θ with the normal. Since the sum of angles in a triangle must equal 180 degrees, the angle between the reflected ray and the refracted ray must be 90 degrees.
As an example, suppose light is incident upon a glass surface from air. Assuming the refractive index of glass (ℓ) is 1.5 and that of air (ℓi) is 1, the Brewster's angle for glass surface could be calculated as tan-1(1.5/1) which is approximately 56.3 degrees. If we have light incident at this angle, the reflected and refracted rays would indeed be at right angles to one another.