The critical angle for an air-glass interface is 42.6°. A light ray in air hits the interface, and the reflected ray is 100% polarized. What is the angle of refraction for that ray?

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Quizplus · Accepted Answer

When a light ray is 100% polarized upon reflection, it means that the angle of incidence is the Brewster's angle. The Brewster's angle ($\theta_B$) and the angle of refraction ($\theta_r$) are related by $\theta_B + \theta_r = 90^\circ$. Given the critical angle is 42.6°, which is relevant for total internal reflection and not directly for polarization, we use the fact that at the Brewster's angle, the light is polarized, and the reflected and refracted rays are perpendicular. Therefore, if the angle of incidence is the Brewster's angle, then the angle of refraction is $90^\circ - \theta_B = 90^\circ - 42.6^\circ = 47.4^\circ$. However, this calculation mistake leads to an incorrect interpretation. The correct approach involves understanding that the Brewster's angle condition implies the relationship between the angles, and without the direct value of the Brewster's angle or a direct calculation involving the indices of refraction, we cannot accurately conclude the angle of refraction from the provided information. The correct answer should involve understanding the principles of light polarization and refraction, but without additional information or a clear connection to the critical angle, the calculation provided is incorrect. The correct approach would involve using Snell's law or the Brewster's angle formula to find the relationship between the angles of incidence, refraction, and polarization properties. My explanation mistakenly attempted to directly relate the critical angle to the Brewster's angle without a basis for doing so in this context.

The Critical Angle for an Air-Glass Interface Is 42 65.7∘65.7 ^ { \circ }65.7∘

The Critical Angle for an Air-Glass Interface Is 42 $65.7 ^ { \circ }$