A laser beam reflected from a horizontal glass surface is found to be totally polarized when the angle of incidence of the beam is 57 degrees. What is the angle of refraction of the transmitted beam in this case?
A) 29°
B) 43°
C) 33°
D) 40°

Question

Quizplus · Accepted Answer

The angle of incidence at which the reflected light is completely polarized is known as Brewster's angle. At Brewster's angle, the reflected and refracted rays are perpendicular to each other. Using Snell's law, $n_1 \sin(\theta_i) = n_2 \sin(\theta_r)$, where $n_1$ and $n_2$ are the refractive indices of air and glass respectively, $\theta_i$ is the angle of incidence (57 degrees), and $\theta_r$ is the angle of refraction. Since the refractive index of air is approximately 1 and assuming the refractive index of glass to be around 1.5, we can calculate the angle of refraction. However, knowing the exact values of the refractive indices is not necessary if we understand that at Brewster's angle, the relationship between the angle of incidence ($\theta_i$) and the angle of refraction ($\theta_r$) can be directly derived from the fact that they are complementary in this specific scenario (since the reflected and refracted rays are perpendicular). Thus, if the angle of incidence is 57 degrees, the angle of refraction would be 33 degrees to satisfy the condition that the sum of angles in a right triangle is 90 degrees.

A Laser Beam Reflected from a Horizontal Glass Surface Is