Light is incident at the Brewster angle on a plastic plate in air.The angle of refraction is 35.0°.
-Determine the Brewster angle.
A)35.0°
B)55.0°
C)46.5°
D)43.5°
E)82.3°

Question

Quizplus · Accepted Answer

The Brewster angle ($\theta_B$) is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When light is incident at the Brewster angle, the angle of incidence ($\theta_i$) and the angle of refraction ($\theta_r$) are related by the equation $\tan(\theta_B) = n$, where $n$ is the refractive index of the refractive material relative to the medium it is entering from. Given the angle of refraction is 35.0° in air (with a refractive index of 1), we can use Snell's law, $n_1 \sin(\theta_i) = n_2 \sin(\theta_r)$, where $n_1 = 1$ (for air), to find the refractive index $n_2$ of the plastic. Since $\theta_r = 35.0°$, we can solve for $n_2$ and then use $\tan(\theta_B) = n_2$ to find the Brewster angle. The correct answer, without needing to perform the calculations, is based on the principle that the Brewster angle for a given material combination is unique, and knowing the angle of refraction allows us to determine it through the relationship between the refractive index and the Brewster angle. Given the options and understanding the relationship between the angles and refractive indices, the Brewster angle is best approximated by the option that reflects this understanding, which is 55.0°, assuming typical refractive indices for plastics and the nature of the Brewster angle.

Light Is Incident at the Brewster Angle on a Plastic