Unpolarized light in air is reflected from a piece of flat glass at an angle of 58 $\circ$ with respect to the normal.The reflected light is found to be completely polarized after the reflection.What is the index of refraction of the glass?

Question

Quizplus · Accepted Answer

When unpolarized light is reflected at a certain angle, it becomes polarized if the angle is equal to the Brewster's angle given by θ_B = tan⁡(θ_i), where θ_i is the angle of incidence. In this case, θ_i = 58°, so θ_B = tan⁡(58°) = 1.54°. At this angle, the reflected light is completely polarized, which means that the reflected electric field vector is perpendicular to the plane of incidence.

Using Snell's law, we can relate the indices of refraction of the air (n_air) and the glass (n_glass) to the angle of incidence and the angle of refraction:

n_air sin⁡θ_i = n_glass sin⁡θ_r

Since the reflected light is polarized, we know that θ_r = 90° - θ_i = 32°. Substituting these values, we get:

n_glass = n_air sin⁡θ_i / sin⁡θ_r = 1.6

Therefore, the index of refraction of the glass is 1.6, which is closest to choice D.

Unpolarized Light in Air Is Reflected from a Piece of Flat